In Chess960 you can castle if your king is in either of the two center squares on your first row and only if then you have one or more of your rooks in a corner on your first row. In some setups you cannot castle. To win you need to think about how to efficiently free up trapped rooks and your queen in a protective organized fashion. Often the computer will leave a rook trapped for too long which can give you the edge that you need to win. Another great thing about chess960 for the human player is the fact that that the computer has no programmed opening moves like most chess computers do for regular chess. You and the computer will both have to think during opening moves.

You can castle in all positions of Chess960. For 0-0-0 the king castles to c1 and the rook from that side wraps around to d1. For 0-0 the king castles to g1 and the rook from that side wraps around to f1. To execute the castling moves either drag and drop the king on top of the rook or click the castling buttons provided on the interface. Be careful that you do not move the king only one square to get it to c1 such as from b1 or d1 because that will be interpreted as a king move only. And be careful that you do not move the king only one square to get it to g1 such as from f1 because that will be interpreted as a king move only. So long as you move the king two squares or drop it on top of the rook or use the castling buttons you can castle in every position.

Indeed. Castling is exactly what makes mirror-image positions distinct in Chess960. Without it, there would be only 480 distinct starting positions.

Indeed, there is a variant called Chess 480, which actually has the same 960 positions, but different castling rules causing mirror-image positions to be completely equivalent.

http://en.wikipedia.org/wiki/Fischer_Random_Chess#Chess_480

You said "a variant" and "different castling rules". Those are not accurate statements simply because there are multiple definitions of Chess480. The only reason there are different castling rules is because that idiot John Kipling Lewis tried to invent new castling rules. Chess480 can be played with the same castling rules as Fischerandom/Chess960. The difference between Chess480 and Chess960 is that 480 of the positions are ruled out while castling remains the same.

Are you going by your interpretation of the Wikipedia article or from an understanding you already had?

What I'd thought it to mean is that Chess480 is defined as having the different castling rules described in the first paragraph of that section, with the "other definitions" being merely methods of having only 480 starting positions under these rules, rather than 960 positions only half of which are distinct.

Chess480 as I understand it has the same castling rules that Fischer invented. I don't like the castling rules John Kipling Lewis invented. The point of the last paragraph is that there are many ways of dividing up the two halves of Chess960.
A while back, at chessvariants.com, I challenged JKL to state what distinguishes one set of 480 positions from the other in his definition. He could not do it. Now I understand by the way you have phrased it that it does not matter what orientation left/right the initial position has--what matters is that JKL's castling rules eliminate the difference.
If one uses Fischer's castling rules, one must come up with a criteria by which 480 of the positions are set aside.

Where are the rules of chess 960.