I think opening theory kind of goes out the window in 960 gameplay, though I must confess I definitely don't speak from experience. Of course, knowing what to do in an opening will help you considerably, but the emphasis on middlegame knowledge and tactics is much more pronounced.
I say you should play the opening like you normally would, but make to sure to pay attention to where exactly your pieces are so you can get an idea of what to do.
For example, castling is usually not as "defensive" in this mode as it is normally, because the king and rook will almost never be in their "correct" places. Instead, use it as a surprise attack: try to sneakily obtain an open file or threaten some nasty stuff with your castling. I was looking at one of Hikaru's 960 games the other day and his opponent did this quite well, sacrificing a rook to "castle" in a matter such that Hikaru would get checkmated on the next move if he took the rook (which he didn't do, but still).
Also, brush up on your tactics really well, because they'll typically be even more prevalent due to the potential positions in the game being even more unpredictable than usual.
I've been playing pretty well regular chess lately, but I tried out some unranked chess960 and was playing abysmal. I know I blundered quite a lot because I really didn't understand the random positions it was giving me, causing me to mess up opening principals. Anyone have any tips?