You and fellow players are dealt two cards each whilst the dealer is dealt one face up. If your first 2 cards add up to 21 (an Ace and a card valued 10), that's Blackjack! If they have any other total, decide whether you wish to 'draw' or 'stay'. You can continue to draw cards until you are happy with your hand.
The name of the game is to beat the Bank, in the person of the Dealer, without exceeding 21. Otherwise you lose your bet. If you reach a Blackjack (21) your bet is multiplied by 3. If you beat the Dealer without reaching 21, you win double your bet.