How the Game is Played
1.) Two sets of cards (consisting of two cards each) are dealt out: One set to the Player; the other set to the Banker.
2.) Any hand totaling 9 or 8 is an automatic winner. 
3.) If additional cards are required, the players hand always draws first.

The Object of Baccarat
Draw 2-3 cards to get a points value as close to nine as possible; and correctly guess which of three events will happen the next round: Player wins, Banker wins or a Tie occurs. 

The Winning Hand
A hand that totals nine in the first two cards. Eight is the second-highest hand. Those two hands are considered "natural" hands. More formally "le grande natural" if it is a nine and "le petit natural" if it is an eight. A natural nine beats a natural eight. If any player hand or the Bank has a natural eight or nine, the other players may not draw a third card. 

Values
All numbered Cards, 2 through 9, are counted at face value. The Ace is counted as one. Tens and all face cards are counted zero. Hands that add up to more than 9 are counted by the second digit only (14 would be counted 4), so that 9 is the highest possible score. 

Additional Cards
If neither hand is a natural (8 or 9), each hand is required to receive an additional card. The Banker's next action (drawing or standing) depends on the player hand total. This gives you a slight advantage.
Here is an example of how the cards are dealt:

Commission
American Baccarat: A 5% Commission is exacted on a winning banker bet, but not on any losses. So if you win $100, you owe the house $5. Rather than collecting this commission after each round, a record of what is owed by each player is kept on the table in a numbered box. Usually, players pay after the finish of each shoe and before leaving the table.
European Baccarat: The banker finances the round; this gives him a slight edge over the player´s hand. Example: Banker funds $1,500. Next player bets $1,000. The next player is allowed to bet $500 only. The next players are not allowed to bet now any more. if a player wants to cover the entire banker's bet, he calls out "banco". No other player is allowed to bet during that specific round.

The Tables

Traditional Baccarat Table

Full staff of three tuxedo-clad dealers on a large table that allows 12 to 14 players. The number 13 is eliminated to accommodate any superstitious beliefs of unluck.
Played in an area normally reserved for high rollers, with minimum bets of $100 to $500 and maximum bets of $50,000 per hand. Strict dress code for customers. 
The game is relaxed and slow: about 50 to 70 hands or rounds per hour.

Mini-Baccarat Table

Minimum table limits range from $2 to $10. 100-150 hands or rounds per hour. Cards are dealt from a 6- or 8-deck shoe by a single dealer. The players do not handle the cards.