All the rules of regular chess apply. However, a player can win by checking the other player three times, not necessarily consecutively. Regular checkmate also wins the game.
We will provide each player with three tokens of the opponent's color to keep count of each check. However, verbally announcing "check" is not recommended.
PLACEHOLDER
There are no more rules to give for this variant. The rest of this document is concerned with giving suggestions for strategy. Your own study of this variant might suggest better strategies than the ones given here.
For the opening, White should avoid the queen's pawn opening (1. d4) and the Mieses opening (1. d3), because Black might try to play 1. ... e6 or 1. e5 in the hopes of playing 2. ... Bb4+ next.
It is better for White to start with the king's pawn opening (1. e4) or the van't Kruijs opening (1. e3), because if Black plays 1. ... d6, d5, f6 or f5, White can then play 2. Bd5+ or 2. Qh5+.
Generally, you want to give the first check. If you can quickly follow that up with a second check, even if you lose the attacking piece, you're in much better shape to win the game than your opponent. In that situation, your opponent would need to get two checks against you to catch up, all the while fending off other check attempts.
Castling is a good idea even if your opponent is getting to deliver a check to your king in his castled position, given that such an attack is likely to be a sacrifice, especially if you've already gotten one or two checks in and this would be your opponent's first check.
It's nice to win with checkmate, but if you can win with a third check, you should go for it, even if it would be a pointless sacrifice in a regular chess game.