There are two hands played in Baccarat - the "player" hand and the "banker" hand.  You can bet on either one.  If the hand you bet on wins, you receive an even money (1:1) payoff.  There is one other bet you can make - the tie bet.  If you make this bet and the two hands tie, you receive an 8:1 payoff.  Ties, however, occur less than once out of every ten hands.

At the start, each hands receive 2 cards.  When necessary, additional cards are drawn according to the rules.  The hand closest to 9 wins. 

10s, Jacks, Queens, and Kings all count as 0.  The ace through 9 cards have face values of  1 to 9, respectively.  To determine the value of each hand, you simply add the cards.  If the total is over 10, the first digit is ignored.  So an 8 and a 6 would normally equal 14, but since we disregard the first digit, we instead have a hand of 4.  Similarly, a 6 and 4 would equal 0, and a 10 and 9 would equal 9.

If the first two cards total 9, the hand is called a "natural" and automatically wins.  Two cards totaling 8 is also referred to as a natural, and it wins automatically too, unless the hand it is playing against has a natural as well.  When both hands contain a natural, the higher natural hand wins (9 beating an 8)  If the hands have equal value, it is a tie. 

When neither hand has a natural, there is no automatic winner, and additional cards are drawn to determine the outcome of the hand.