Fill-in-the-blank clues are often the easiest in a puzzle and a good place to start solving, e.g., "_____ Boleyn" = ANNE.
"Before and after" clues feature one word that is part of two phrases, often designated with parentheses and brackets, e.g., (Doing [____) keeper] = TIME.
A question mark at the end of clue usually signals that the clue/answer combination involves some sort of pun or wordplay, e.g., "Grateful?" = ASHES, since a grate might be full of them.
Most widely-distributed American crosswords today (e.g., The New York Times, Washington Post, Boston Globe, USA Today, etc.) also contain colloquial answers, i.e., entries in the puzzle grid that try to replicate everyday colloquial language. In such a puzzle one might see phrases such as WHAT'S UP, AS IF, or WHADDYA WANT.