Learn chess notation. This is a method of recording the moves of a game. It's easy to learn, and it will help you out here.
If you record the moves of the game, then if you suspect him of cheating, then you can always go back to the beginning of the game and replay the moves, thereby arriving at the correct current position.
The King always starts on the opposite of his own color. The Queen always begins the game on the center square of her own color.
Castling can be done in certain circumstances. All of the following must be true in order to be able to castle.
1) The King must not have been moved yet. If the King moves and later moves back to its original square, it can not castle.
2) The rook used for castling must not have moved. If it does move and later moves back ot its original square, it still can not be used in castling.
3) The King can not castle if it is in check. If the King can escape check without moving, it can then castle later in the game.
4) The King can not castle into check...in other words, it can not end a castling move on a sqaure that is exposed to attack by the enemy.
5) The King can not castle "through" check...in other words, it can not pass OVER any squares that are attacked by the enemy during a castling move.
6) Finally, ALL squares between the King and the Rook must be UNOCCUPIED.
In order to castle, you move your King two squares in the direction of the Rook being used in the castling move. The rook is then placed on the other side of the King. You'll notice that the King starts the game four squares away from one Rook (separated by a Queen, Bishop and Knight), and three sqares away from the other rook (separated by a Bishop and a Knight).
To castle with the "Queen Rook", move your King two squares toward that rook, and place the Rook on the square that the Queen originally started on. (The King is placed on the square originally occupied by the Bishop).
To castle with the "King Rook", move your King two squares toward that rook, and place the Rook on the square originally occupied by the Bishop at the start of the game. (The King is placed on the square originally occupied by the Knight)
The idea of the opening is to do the following:
1) Move no more than one or two pawns, preferably the center pawns.
2) Control the center of the board (put your pieces so that they attack the center squares).
3) Develop your pieces, first the Knights, then the Bishops
4) Castle, in order to protect your King and unite your Rooks
5) Try to prevent your opponent from doing these things (not always possible).
You are not required to say "Check" when attacking your opponent's King. It is their responsibility to see the check and react to it. However, a rule you should be aware of:
1) If your King is in check, and you move another piece that doesn't address the check, you are required to take the move back, and you are required to use the piece that was moved illegally to stop the check, if it is possible to do so. If it is not possible to move the piece without answering the check, then there is no penalty. The move is simply taken back, and the check must be answered.
In tournament rules, tipping your King over is a way of surrendering. In friendly games, there is no penalty.
I just googled "How to Play Chess" and there are plenty of sites to teach you the basics.
Here's one such site:
http://www.soyouwanna.com/site/syws/chess/chess.html
If you have a few bucks to spend on books, I would recommend that as well. Start with Susan Polgar's two books, "A World Champion's Guide to Chess" and "Chess Tactics for Champions". You can set up the different positions shown in these books on your chessboard and play through them, that will give you a better feel for the game.
There is a reason to keep playing even if you lose a number of pieces early. Number 1, you can learn more in games you lose than in games you win, and Number 2, there's always a possibility that your opponent could get careless and stalemate you, which would mean the game would be drawn. Stalemate occurs when your King is NOT in check, but you have no legal moves available (i.e. any move you make would expose your King to check). Stalemated games are a draw, regardless of the superiority of one side over the other in terms of forces left on the board.
Chess has been around for more than 1,500 years...the moves of the pieces have remained the same for the past 500 years or so (the Queen and Bishop did not always move as they do now, but the King, Knight and Rook have always moved in the same way).
One other thing you can do...next time your bf cheats, throw HIM off of the 3rd floor balcony...that'll teach him.
Good luck to you!