Punctuation is the name for marks used in writing text. They are to help understanding and the correct reading. These are some common punctuation marks used in English:

 . is a period or full stop
 , is a comma
 ? is a question mark
 ! is an exclamation mark
 ' is an apostrophe or single quote mark
 " is a quotation mark/inverted comma
 : is a colon
 ; is a semicolon
 ... is an ellipsis mark
 - is a hyphen
  is an en dash
  is an em dash
 ( ) are parentheses or curved brackets
 [ ] are brackets or square brackets.
There are other punctuation marks but used less often. Other languages have other marks, such as French using guillemets, « » as quotation marks.

Rules of punctuation 
The use of punctuation in English can change from place to place and from time to time, for the rules in use at that location. Modern typography suggests that punctuation should only be used when there is a need. That results in less punctuation than was the case in the early 20th century.

The use of these marks is often decided by a group or organization and then written down into a style guide of format rules. Newspapers have a style guide to make their content use the same rules (for consistency).

Reasons for punctuation 
One reason is obedience. If we work for an organization with a house style guide, then we use that guide. 
Punctuation helps the reader understand what is meant. Consider these examples:
He did not go to town because his father was absent. This means he did go to town, and the reason was not his father's absence.
He did not go to town, because his father was absent. This means he did not go to town, and the reason for not going was that his father was absent.
In the second example, no style guide will help. The writer just has to make sure that the sentence is understood as it is written. Punctuation is there to help the reader make sense of what is written. Often it is best to change the sentence so that the meaning does not rest on a comma.
He went to town, but not because his father was away. 
Because his father was away, he did not go to town.
That seems to make the meanings clear.

Period or full stop 

A period (U.S.A.), full stop (U.K. and Commonwealth) or full point (typography and printing), looks like this: .

A period or stop is used to end a sentence. The period plus a space separates sentences in prose, and makes it easier to read. If they are not needed, they should not be used. So, for example, in a list format it is obvious when a section ends, therefore it does not need a full stop.

A period can show numbers that are smaller than one. With money, a period is used to show the amount of money less than one dollar.

For example: "Elizabeth bought a soda for $1.25." means that Elizabeth paid one dollar and twenty-five cents for her drink.

A period is sometimes used to show that a word has been made shorter. A word that is made shorter with a period is called an abbreviation.

For example: The words doctor or mister are often made shorter when used with a name. "Dr. Smith" is the name of a doctor whose last name is Smith, and "Mr. Banerjee" and "Mrs. Yang" are common ways of writing. However, in modern typography, plain "Mr, Mrs/Ms" or "Dr" are more common. "Mrs" is never written in full: to write  "mistress" is to mean something quite different. See also capitalization.

Comma

A comma looks like this: ,

A comma has many uses. Some of these are shown below:

To separate things in a list: "cows, horses, pigs, and sheep". A comma that is used before the word and in a list is called an Oxford comma. Some people do not use Oxford commas: "cows, horses, pigs and sheep".
To separate two sentences with a conjunction: "Most birds have separate toes, but ducks' feet are webbed."
To separate parts of a sentence: "Mimi, hungry as she was, was shy to come forward and have a slice of cake."
To indicate a pause in a sentence or question: "Hallie, did you remember to feed the cat?"
In some European countries, commas are used as the -Insert number base here- point, instead of a full stop. Instead of €3.57 it would be €3,57. In an inverse to that, €17,693 (Seventeen thousand, etc.) would be €17.693.

Question mark

A question mark looks like this: ?

Question marks are used when writing a question, to make an inquiry, or to ask something.

For example:
"Hallie, have you done your homework?"
"Elizabeth said 'How are you?' to Hallie."
"Why is the sky blue?"
"Do you like apples?"

Exclamation mark

An exclamation mark looks like this: !

An exclamation mark is used to write about a suprise or emotion, or to write the words a person shouted. It can be used to make a statement stronger or more forceful.

For example:
"What a bad cat she has!"
"Jane, come here!"
"You did a good job!"
How wonderful this city is!
Don't talk, get out!
And also an exclamation mark can be used with a question mark, to make a question more forceful.
For example:
"What did you do that for?!" she said angrily.

Apostrophe

An apostrophe looks like this: '

An apostrophe has two main uses:

Ownership
An apostrophe can be used to show that something belongs to someone else.

If there is only one thing, the letter s is used after an apostrophe to show ownership.

For example:
"It was the boy's dog."
"We will go in Mimi's car."

Sometimes the letter s is not used after an apostrophe to show ownership. A word will end with just an apostrophe if there is more than one thing and the word already ends with an s.

For example:
"Father put away the girls' clothes" means that Father had to tidy up for several girls.
"Father put away the girl's clothes" means that Father tidied up for only one girl.

Contractions
An apostrophe can be used to put two small words together. Two small words that are put together with an apostrophe to make one word are called contractions. This is normal in writing about a person speaking. Spoken English often uses contractions because these words are easier to say.

For example:
Cannot can be made into the word can't.
It is can be made into the word it's, for example, "It's a nice day today."

Common mistakes when using apostrophes
Pronouns do not use an apostrophe to show that something belongs to something else. Among these are its, his, hers, theirs.

For example:
"The bird flapped its wings," not "The bird flapped it's wings."
"It is his bike," not "It is his's bike."

Plurals (words referring to more than one thing) do not need an apostrophe.

For example:
"Apples for sale," not "Apple's for sale."

Quotation marks

Quotation marks (also called quote marks or quotes for short) are used around the words that people have said, or direct speech. They are used in pairs.

For example:
Hallie said, "Mimi, please wash the dishes."
"Today," said our teacher, "is the first day of the rest of your lives."

Example:
"After recording 'Beat It', Michael Jackson went on to record several more hits".

Order of punctuation 
When quotation marks sit next to periods and commas, there are two styles of punctuation. These two styles are most commonly referred to as "American" and "British"; the British one is also called "logical quotation".

Both systems have the same rules regarding question marks, exclamation points, colons, and semicolons. But they differ in how they treat full stops and commas.

In all major forms of English, question marks, exclamation marks, semicolons, and any other punctuation are placed inside or outside the closing quotation mark depending on whether they are part of the quoted material.

Did he say, "Good morning, Dave"?
No, he said, "Where are you, Dave?"
There are three major definitions of the word "gender": vernacular, sociological, and linguistic.

British practice 
The style in the United Kingdom and other non-American places is called British style, 
logical quotation, 
or logical punctuation. it includes inside quotation marks only those punctuation marks which appeared in the original quoted material. Otherwise it places punctuation outside the closing quotation marks. Fowler's A Dictionary of Modern English Usage provides an early example of the rule: "All signs of punctuation used with words in quotation marks must be placed according to the sense."
When dealing with words-as-words, short-form works and sentence fragments, this style places periods and commas outside the quotation marks:
"Carefree", in general, means "free from care or anxiety".
The name of the song was "Gloria", which many already knew.
She said she felt "free from care and anxiety".

With direct speech, British placing depends on whether or not the quoted statement is complete or a fragment. According to the British style guide Butcher's Copy-editing, American style should be used when writing fiction. In non-fiction, some British publishers may permit placing punctuation that is not part of the person's speech inside the quotation marks but prefer that it be placed outside. Periods and commas that are part of the person's speech are permitted inside the quotation marks regardless of whether the material is fiction.
"Today," said Cinderella, "I feel free from care and anxiety." (fiction)
"Today", said the Prime Minister, "I feel free from care and anxiety." (preferred in non-fiction)
"Today I feel happy," said the woman, "carefree, and well." (regardless)

U.S. practice 
In the United States, the prevailing style is called American style, whereby commas and periods are almost always placed inside closing quotation marks. This style of punctuation is common in the U.S. and to a lesser extent, Canada as well., and is the style usually recommended by The Chicago Manual of Style  and most other American style guides.

When dealing with words-as-words, short-form works and sentence fragments, standard American style places periods and commas inside the quotation marks:
"Carefree," in general, means "free from care or anxiety."
The name of the song was "Gloria," which many already knew.
She said she felt "free from care and anxiety."

This style also places periods and commas inside the quotation marks when dealing with direct speech, regardless of whether the work is fiction or non-fiction:
"Today," said Cinderella, "I feel free from care and anxiety." (fiction)
"Today," said the Prime Minister, "I feel free from care and anxiety." (non-fiction)

Ending the sentence 
In both major styles, regardless of placement, only one end mark (?, !, or .) can end a sentence. Only the period, however, may not end a quoted sentence when it does not also end the enclosing sentence, except for literal text:
"Hello, world," she said. (American style)
"Hello, world", she said. (British non-fiction)
She said, "Hello, world." (both styles)
"Hello, world!" she exclaimed. (both styles)
"Is anybody out there?" she asked into the void. (both styles)

Colon

This is a colon: :

Colons can be used at the beginning of a list. "This is a list of animals: birds, cats, insects, pigs, and sheep.".

Colons can be used to replace a semicolon in between two parts of a sentence, but this is not common today.

Standard English usage is to have no spaces before, and one space after a colon.

Semicolon

A semicolon looks like this: ;

A semicolon has only two uses.  First, to connect two independent clauses into a single sentence.  For example:
"I could tell that it was getting late; it was growing darker by the second."
The second use of a semicolon is to separate items in a series when the items contain parenthetical elements within themselves.  For example:
"The following crewmembers were on the bridge: James T. Kirk, captain of the
Enterprise; Mr. Spock, first science officer; Mr. Sulu, helmsman; Mr. Scott,
engineer; and Dr. McCoy, chief medical officer."

A semicolon is also used with a conjunctive adverb when joining two clauses.  In reality, this is the same as the first rule, but it looks different enough to sometimes cause concern.
For example:
"huzaifa, context in which all life exists; consequently, it is more than a political issue."

Ellipsis

An ellipsis is a mark that looks like this: ...

It is used to show where words have been omitted when writing what a person said. It can also be used to show that there is more to be said but the person stopped at that point.
For example:
... one day all Americans will live peacefully throughout the world ... they will be at peace with all other world inhabitants ...
So much more could be said ...

Hyphen

A hyphen looks like this: -. Hyphens have many uses in writing:

 Some words can have a hyphen added to change the meaning. For example, re-form means "start again" but reform means "change". A re-formed group is different from a reformed group.
 A hyphen is used to spell out some numbers (thirty-two, forty-nine, eighty-six).
 When a name for a material such as "stainless steel" is used with a word for a thing made of that material, a hyphen is used, as in "stainless-steel knife".
 Some words have letters at the beginning, or prefixes, these can sometimes use hyphens: un-American, anti-pollution, non-proliferation
 When spelling out a word: H-Y-P-H-E-N
 In some cases, when putting two words together would be hard to understand. For example, if something is like a shell, writing it as "shelllike" is hard to read with so many uses of the letter 'l'. It is better to use "shell-like."
 When writing words that someone has spoken when that person has difficulty speaking, as in: "I reached for the w-w-w-watering can." This is called a stammer.
 When adding words that already have a hyphen. For example: two to year-old as in: "He was a two- or three-year-old dog."
 If a word for a person (a name or proper noun) is used with another name, a hyphen is used such as "the Merriam-Webster dictionary" or "the Molotov-Ribbentrop Pact."
 Some people take a name from the family names of both parents, or from the last name of their father and spouse. For example: "John Rees-Williams". This is not always the case, for example: "Hillary Rodham Clinton".
 A hyphen is also used when a word is too long to fit in one row of writing. This is often done in books, magazines and newspapers to save space and paper. A long word is broken into two parts, of nearly the same length, with a hyphen at the end of the first part. The normal way is to make the first part of the word as much like a complete word as possible. For example:

References

Bibliography
Trusse, Lynne 2003. Eats, shoots, and leaves. Profile Books.
Carey G.V. 1946. Mind the stop: a brief guide to punctuation with a note on proof-correction. Cambridge University Press,