Sorry but I'm afraid it is not possible to study openings for chess960, because you would have to memorize 960 times more than regular chess. But if you want to get better, you should practice tactics, positional play and endgames for normal chess because it works the same way.
Hi! In the opening you should still try to occupy the center, develop all your pieces and castle. At the first move check, which of your pawns are not defended at well. Protect them and look for chances to grab unproteced pawns of your opponent.
If minor pieces (specially bishops) start in a corners, give them priority in development to avoid them being stuck there. Conversely, if your opponent is neglecting a corner piece, try to push pawns to impede its development. The Stockfish code for chess 960 has an evaluation term tacked on for corner bishops.