Castling in chess--queen side or king side

It depends on the position and what kind of game you're going for. Generally, queen side castling is more aggressive since it places the rook right in the center while king side castling puts it in a more passive position on the f file and you need to expend an extra move putting it in the center. Castling queen side OTOH leaves the a pawn exposed and you'll need to spend a move putting the king on b1 to protect it.

Generally speaking, if both players castle on the same side of the board, it more often leads to a closed, positional game while castling on opposite sides leads to a more open, tactical game. There isn't really a clear-cut advantage to either king or queen side castling, but the former is more common simply because you can do it quicker.

In some situations, you can skip castling altogether, generally in a closed position with locked center pawns, the king can be left in the center safely and this may also be an advantage in the endgame. In e4 e5 openings, not castling tends to end poorly.

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Which side of the board to castle on depends on several things, for example if one side has a large concentration of enemy pieces, you don't want to castle there. Also it goes without saying that you shouldn't castle if the pawn structure on that side of the board is ripped up.