Anagrams: The letters of the answer are scrambled into one or more words within the clue - "Icy Spanish stew for doctors (10)" yields the answer PHYSICIANS, an anagram (mixture, or "stew") of "icy Spanish."
Charades: The answer is broken into two or more parts, each of which is given or clued - "Deer and insect run off (8)" yields ANTELOPE, formed by "ant" and "elope."
Containers: Similar to Charades, but the components are one within the other - "Uncle captivated by caressing child (9)" yields FOUNDLING, which is "U" (abbr. of "uncle") inside "fondling."
Deletions: The answer is derived by removing one or more letters from a longer word or phrase - "Transmitters lead off with 'goodbye' (5)" yields ADIOS, produced by taking the "lead" (first letter) off "radios."
Double Definitions: Two distinct meanings (and possibly pronunciations) of the answer are defined - "Was very friendly, but lost interest (6)" yields PALLED, pronounced first /pald/, then /pôld/.
Hidden Words: The answer appears camouflaged by a word or phrase in the clue - "Manager in comic opera (5)" yields COPER (one who copes, or manages), seen in comicopera.
Homophones: The answer sounds exactly like another word or phrase - "State police in thicket" (5) yields COPSE, which results if you "state" the word "cops."
Reversals: The answers spells something else backwards - "Love can give you aching back (4)" yields EROS, which is "sore" backwards.
Three additional things must be noted. First, most of these types of clues require words to tell you what types they are. Anagrams have indicators that suggest mixture, wrongness, destruction, etc., as "stew" above. Charade indicators, if any are used (they needn't be), will suggest addition. Container indicators suggest either holding or surrounding, as "captivated." Deletion indicators suggest removal ("off"). Double Definition clues don't need indicators. Hidden Word indicators suggest just that - hiding, or perhaps, fractionality ("in"). Homophone indicators suggest hearing, sound or speech ("state"). Reversal indicators suggest backwardness, or a moving west or north, or a moving left or up ("back").
Second, a clue may use two or more types of wordplay at once. "Sketches in act rarely ended abruptly, in retrospect (7)" works thus: "Sketches" = definition; the word is found in DO ("act") plus SELDOM ("rarely") curtailed ("ended abruptly") and reversed ("in retrospect"), or DO + [m]ODLES = DOODLES.
Third, in a special type of clue known as an "& lit." (short for "and literally so"), the definition and the wordplay are one and the same. "Ingredient in rye - a stimulant! (5)" yields the hidden word YEAST; "Terror's locale, if rickety! (6,7)" yields the anagram ROLLER COASTER; "Softly supplemented! (6)" yields the charade P-ADDED. The exclamation point will often indicate an "& lit." clue.
A special note to beginners: don't be discouraged if you are unable to complete a cryptic crossword. The best way to improve your solving of cryptics is to become familiar with how clues are constructed, and how they lead to the answers. So, feel free to take a peek at the answers as you solve. In any case, always review the answers and explanations for every cryptic crossword you do. With experience, you'll see your solving improve.