Is there some "crypts for dummies" site that y'all could recommend, so I could at least start understanding the answers?
Sure. Plus, if you post a specific clue and answer, someone would be happy to try explain it.
A single cryptic clue can stand alone, as an individual word puzzle, or it can be just one of a set of clues, where the puzzle is to complete an entire crossword grid. The "crypts" posted at this site are standalone puzzles.
In a traditional crossword puzzle, a clue is given, and the solver knows how many letters comprise the answer. For example: 1 Down might be seven letters, with the clue "Makes heads spin". The answer is VERTIGO.
In a cryptic clue, "makes heads spin" would still appear, but the clue would also contain additional words. The added words form some type of word play that leads to the same answer. Hence, a crypt contains two clues to the answer; one is stated directly, and the other is a puzzle to solve. (In this way, crypts are like a puzzle within a puzzle, with the direct part of the clue serving as a confirmation of the word-play result.)
Very trimmed and tailless tigon makes heads spin (7)
"makes heads spin" is the direct (i.e., it directly clues the answer VERTIGO).
"Very trimmed and tailless tigon" is the word play, leading to the same answer.
The words 'trimmed' and 'tailless' are called indicators. They indicate some action to be performed, on one or more remaining words/strings, in the word play.
The indicator 'trimmed' instructs the solver to cut-off some letters from a word. Hence, the phrase "Very trimmed" is read as "trim off part of the word: very".
The indicator 'tailless' instructs the solver to remove the last letter from a word. Hence, the phrase "tailless tigon" is read as "remove the last letter of the word: tigon".
The word 'and' indicates concatenation of these two part. (This type of word play is known as 'charades', where an answer is constructed by parts.)
Very trimmed = VER
tailless tigon = TIGO
makes heads spin = the direct
Hence: "Very trimmed and tailless tigon" = VER+TIGO, and the direct (makes heads spin) confirms the answer VERTIGO.
There are several types of word play, and a clue may contain more than one type: charades, anagrams, reversals, words hidden inside larger words or phrases, homophones, deletions, contents/containers, abbreviations, double-definitions, literary presentations (i.e., the entire clue serves as both word play and direct), and others. Different types of word play may be indicated by any one of several dozen possible indicator words for each type.
Solving a cryptic clue involves trial-and-error. One must determine the direct, such that word play may be successfully performed on what remains. The direct always appears at one end of the clue or the other. Solving also involves learning the different types of word play, and recognizing respective indicator words.
Be advised: the rules differ, depending upon whom you ask (eg: British puzzles differ from North-American puzzles, in some of ways). And, like with mathematics, personal opinions on the topic seem strong. I'm still learning! The main point is to have fun.
Here are some links; you can google (eg: cryptic clue examples), for more sites.
https://en.wikipedia.org/wiki/Cryptic_crossword
http://cryptics.wikia.com/wiki/Cryptipedia
http://bestforpuzzles.com/cryptic-crossword-tutorial/index.html
http://alwayspuzzling.blogspot.com/p/cryptic-class.html
