How do cryptic crosswords work?

Normal crosswords simply give a clue that defines their answer. For example, "Feline - 3 letters" would be answered by "cat". Cryptic crosswords clues have various forms but generally they have part of the clue that is a definition and the rest of the clue that hints at the same definition through coded methods like wordplay or anagrams. For example "Smallest half of the alphabet - 4 letters" is solvable as "atom" where "atom" is theoretically the smallest possible particle of an element, and "A to M" is half of the alphabet.