How to win at chess 960 without really trying?

The short answer is "no way": chess 960 is both more challenging and more fun than the normal variety. Here are a few pointers from my experience.

1) You have to start thinking at move #1. Since there is no opening theory, every move must be calculated on the fly.
2) Even more so than in ordinary chess, it is essential to develop quickly.
3) An attack can develop a lot faster and it feels as though the middle game happens much sooner, ie things quickly get interesting. My 960 games are on average 17% shorter.
4) The starting position is often less stable. There may be weaknesses worse than the usual c2/f2, right at the beginning, eg an undefended pawn open to a Bishop attack after one move.
5) Because the initial position is usually more dynamic, White may have a strong advantage with the first move.
6) Extra thought has to be given to castling, including on which side. Castle early! See my blog on castling http://blog.chess.com/soler97/castling-in-chess-960
7) Developing the Bishops may be awkward, eg if they are at a1 and b1.

So put down that bulky opening book and enjoy 960!