Figure Out the Theme
Lots of crosswords have a title that provides some insight into the theme of the puzzle. And, whether or not the puzzle has a title, it will almost always have a theme. Throughout the puzzle, the author will scatter answers that tie back into the theme. Those answers will usually be longer and contain more than one word. Frequently, the clues will be a play on the theme, so the connection might not be immediately obvious. Still, keeping the theme or title in mind as you go through the clues might provide some insight to lead you in the right direction.