Esperanto's grammar (rules of language) is meant to be simple. The rules in Esperanto never change and can always be applied in the same way.

Articles 
Esperanto has only definite article la (the same thing as "the" in English) and no indefinite article (the same thing as "a" or "an" in English). They use definite article when they talk about things, about which they have already told something.

Nouns and adjectives 

Nouns end with -o. For example, patro means father. To make a noun plural add -j. For example: patroj means fathers.

Adjectives end with -a, adverbs end with -e, for example granda means big, bona means good, bone means well.

The -n ending is the mark of the direct object (the Accusative case) in nouns and adjectives. For example:
 Mi vidas vin. - I see you.
 Li amas ŝin. - He loves her.
 Ili havas belan domon. - They have a nice house.

In adjectives and adverbs is comparison made by words pli (more) and plej (most). For example:
 pli granda - bigger
 plej granda - biggest
 pli rapide - faster
 plej rapide - fastest

Pronouns 

 Personal pronouns are: mi - I, ci - thou singular, li - he, ŝi - she, ĝi - it, ni - we, vi - you singular or plural, ili - they, oni - one/they, si (self). The pronoun oni is used for uncertain subject (like man in German). The pronoun ci means thou but people do not use it much. Instead they use vi, almost exclusively, as the singular form of you, or the plural form - you all.
 Possessive pronouns are made by adding of ending -a to a personal pronoun: mia - my, cia - your singular, lia - his, ŝia - her, ĝia - its, nia - our, via - your plural, ilia - their. People use possessive pronouns like adjectives.
 Accusative case (the -n ending) is used in pronouns as well: min - me, cin - thee, lin - him, ŝin - her, ĝin - it, nin - us, vin - you or you all, ilin - them.  As noted with ci, cin is very seldom used in modern spoken Esperanto.

So, to say how old somebody is in Esperanto, just say:
 Lia aĝo estas dudek = He is twenty (20) years old. (word for word: His age is twenty (20).)

Verbs 

Verbs end with -as when they are in present tense. English uses I am, you are, he is. But in Esperanto, there is just one word for am, are, is - estas. Similarly, kuras can mean run or runs. Infinitives end with -i. For example, esti means to be, povi means to can. It is easy to make past tense - always add -is ending. To make future tense, add -os. For example:
 kuri - to run
 mi kuras - I run
 vi kuras - you run
 li kuris - he ran
 ĝi kuros - it will run

Many words can be made opposite by adding mal at the beginning.
 bona = good. malbona = bad
 bone = well, malbone = poorly
 granda = big, malgranda = small
 peza = heavy, malpeza = light

Examples of sentences which show the rules:
  = I can run fast.
  = You cannot run fast.
  = I am a boy.
  = I am a bad Esperantist.

Yes/No questions 
To make a yes-or-no question, add Ĉu at the beginning. For example:
  = Do you speak Esperanto?
  = Yes, I speak Esperanto very well.
  = No, I am a beginner.

Unlike in English, they can answer to a yes/no question only jes (yes) or ne (no).

Numbers 
The numbers are:

Numbers like twenty-one (21) are made by their compounding by order of magnitude. For example: dek tri means thirteen (13), dudek tri means twenty-three (23), sescent okdek tri means six hundred eighty-three (683), mil naŭcent okdek tri means (one) thousand nine hundred and eighty-three (1983).

Prefixes and suffixes 
Esperanto has over 20 special words which can change the meaning of another word. People put them before or after the root of a word.

These words combined can make very long words, such as malmultekosta (cheap), vendredviandmanĝmalpermeso (prohibition of eating a meat on Friday).

Prefixes 
Prefixes are added before the root of the word.
 bo- – means "in-law". Patro means father, and bopatro means father-in-law.
 dis- – means "all or many directions". Iri means to go, and disiri means to go in different directions.
 ek- – means "start" of something. Kuri means to run, and ekkuri means to start running.
 eks- – makes the word "former". Amiko means friend, and eksamiko means former friend.
 fi- – makes the word worse. Knabo means boy, and fiknabo means bad boy; odoro means smell, and fiodoro means bad smell.
 ge- – changes meaning of a word to "both gender". Frato means brother, and gefratoj means brother(s) and sister(s).
 mal- – makes the word opposite. Bona means good, and malbona means bad.
 mis- – means "wrong". Kompreni means to understand, and miskompreni means to understand wrong.
 pra- – means "prehistoric", "very old" or "primitive". Homo means human, and prahomo means prehistoric human.
 re- – means again. Vidi means to see, and revidi means to see again.

Suffixes 

Suffixes are added after the root of the word, but before the ending.
 -aĉ- – makes the word uglier. Domo means house, domaĉo means ugly house.
 -ad- – means continuous doing of something. Fari means to do, and Faradi means to do continuously.
 -aĵ- – means a thing. Bela means beautiful, and belaĵo means a beautiful thing; trinki means to drink, and trinkaĵo means a drink ("something for drinking").
 -an- – means member of something. Klubo means club, and klubano means a member of a club.
 -ar- – means many things of the same kind. Arbo means tree, and arbaro means forest.
 -ĉj- – makes male diminutives. Patro means father, and paĉjo means daddy.
 -ebl-– means ability or possibility. Manĝi means to eat, and manĝebla means eatable.
 -ec- – means quality. Granda means big, and grandeco means size.
 -eg- – makes the word bigger. Domo means house, and domego means big house.
 -ej- – means a place. Lerni means to learn, and lernejo means school ("place for learning").
 -em- – means tendency. Mensogi means to lie, and mensogema means with tendency to lie.
 -end- – means something which must be done. Pagi means to pay, and pagenda, means something which must be paid.
 -er- – means a bit of bigger group. Neĝo''' means snow, and neĝero means snowflake.
 -estr- – means a chief of. Urbo means town, and urbestro means mayor ("chief of a town").
 -et- – makes the word smaller. Domo means house, and dometo means small house.
 -id- – means the child of. Kato means cat, and katido means kitten.
 -il- – means instrument. Ŝlosi mens to lock, and ŝlosilo means key (an instrument for locking).
 -ind- – means worthiness. Ami means to love, and aminda means something which is worth to be loved.
 -in- – changes the gender of a word into female. Patro means father, and patrino means mother.
 -ing- – means a holder. Kandelo means candle, and kandelingo means candlestick ("a holder of a candle").
 -ism- – means an ideology or movement. Nacio means nation, naciismo means nationalism.
 -ist- – means somebody who does something (perhaps as a job). Baki means to bake and bakisto means baker; scienco means science, and sciencisto means scientist. Esperantisto means Esperanto speaker.
 -nj- – makes female diminutives. Patrino means mother, and panjo means mummy.
 -obl- – means times. Tri means three, and trioble means three times. It also makes multiples. Kvin means five, and kvinoblo means multiple of five.
 -on- – makes fractions. Kvar means four (4), and kvarono means quarter (one fourth of something).
 -uj- – generally means a vessel. Salo means salt, and salujo means salt shaker ("a vessel for salt").
 -ul- – means person of some quality. Juna means young, and junulo means young person.
 -um-'' is suffix for cases when is not able to do a word from other existing suffixes, preffixes or roots.

References

Linguistics
Esperanto