Baccarat is played in private rooms to separate itself from the other casino games. The players are usually very well dressed and the table minimums are often high. The regular baccarat table is about the size of a craps table with 3 casino dealers and up to 12 or 14 players. Each player, including the player dealing, may still bet on either the player or the banker but it is customary for the dealer to bet on the banker.
The deal will rotate around the table, much like the dice rotate around the craps table. If a player does not want to deal they may pass the shoe to the next player. The same person will keep dealing as long as the banker keeps winning. The person dealing will put two cards, face down, tucked under the shoe, and give the player with the greatest bet on the player the other two cards, face down. This player then looks at the cards and then gives them back to the player who is dealing. Then the player who is dealing will turn over the cards and one of the casino dealers will announce the totals. Depending on the totals the dealer may then instruct the person dealing the cards to deal a third card. Finally the dealers will pay winning wagers and collect losing ones out of the dealer's tray.
The Rules
Baccarat is played with eight decks of cards. Each numbered card less than ten is worth its face value, aces are worth 1, and tens and face cards are worth 0. The suit does not matter.
Play begins by all players betting either on the 'player', 'banker', or a tie. I put player and banker in quotes because that is the correct terminology but they do not necessarily represent the dealer or the actual players.
After all bets are down the dealer gives two cards each to the player and the banker. The score of the hand is the right digit of the total of the cards. For example if the two cards were an 8 and 7, then the total would be 15, and the score would be a 5. The scores will always range from 0 to 9 and it is impossible to bust.
A third card may or may not be dealt to either or both the player and the dealer depending on the following rules.
Player's thirdcardrule
If either the player or the bank have a total of 8 or 9 on the first two cards no further cards are drawn. The resulting hand is called a natural and the hand is over.
If the player's total is less than or equal to 5 the player's hand draws a third card.
If the player does not draw a third card, then the bank's hand stands on 6 or more and takes a third card on a total of 5 or less. If the player does take a third card then the Bank's thirdcardrule below will determine if the bank takes a third card.
Bank's thirdcardrule
If the bank's total is 2 or less then bank draws a card, regardless of what the players third card is.
If the banks total is 3 then the bank draws a third card unless the players third card was an 8.
If the banks total is 4 then the bank draws a third card unless the players third card was a 0, 1, 8, or 9.
If the banks total is 5 then the bank draws a third card if the players third card was 4, 5, 6, or 7.
If the banks total is 6 then the bank draws a third card if the players third card was a 6 or 7.
If the banks total is 7 then the bank stands.
House advantage

Banker (Banco) 
1.17% 
Player (Punto) 
1.36% 
Tie (Standoff) 
14.12% at 8:1 payout 