I’m a crossword freak—totally addicted. I’ve moved to cryptic crosswords recently, and those challenge the brain in new ways. I find them immensely relaxing, as I can take my entire focus to the puzzle and shut out the other noise. It’s one of my life goals to author one of the New York Times themed crosswords for their weekend magazine.
As far as tips—I’d say stay with it. I can remember trying to work my first NY Times puzzle, and it was very frustrating. But over time, you learn the lingo of the puzzle crafters. The more complex puzzles allow you to really exercise your linguistic skills and view possible responses as options if the clue is seeking a verb, a noun, a slang term, etc. See how many solutions you can develop for alternate scenarios and pencil those in.
As with any skill, practice makes perfect.