A player can either move one piece twice or move two different pieces on his turn. Castling is considered as a single move.
When a player gives a check on the first move, he loses the right for the second move on this turn. If a player is in check, he must move out of check on the first move of the turn. It is not allowed to move the king into the check on the first move of the turn and then move out of the check on the second one.
En passant capture is allowed even if the opponent moved the corresponding pawn on the first move of the previous turn. However, en-passant capture must be made on the first move of the turn. When two pawns can be captured en passant after opponents move, both of them can be captured.
To avoid too much advantage for white, usually a balanced version of the game is played. In balanced version white makes only one move on the first turn. The moves are made in the following order: white, black, black, white, white, black, black, etc. This rule was introduced in 1963 by Robert Bruce and since then gained a wide acceptance.