Once you have a few crossing letters in the longer answers, you'll be more likely to get them from their clues. Don't be afraid to guess. At the same time don't be afraid to erase an answer that isn't working out. Don't assume that because you have a few crossing letters that your answer is necessarily correct. And if nothing seems to cross the answer you have filled in, be very wary.
Mental flexibility is a great asset in solving crosswords.
Let your mind wander. I had to inform them gently that the answer was three words, R AND R, as in the time when one goes on leave. A question mark at the end of a clue can mean several things. It can also indicate that the answer only loosely fits the clue. Making a boner may or may not be cause for slapping one's forehead.