-When you put a piece in the right place, it will attach itself to the puzzle and you'll briefly see a couple of white stars. After that, you won't be able to move that piece without moving the entire puzzle. (So if you're not sure if you got the piece in the right place, try to move it. If you can move it without moving the puzzle, it wasn't in the right place.)
-Pencil in lightly any guessed answers. (If solving puzzles online, don't be afraid to enter any guessed answers. They're easily erased with the click of a mouse button.) Then check the crossing entries. If a guessed word contains an uncommon letter such as J or K, check the crossing entries for those letters first.