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.
In blackjack, the value of a player's hand is determined by adding up the values of the individual cards in their hand, while in rummy, the value of a player's hand is determined by the number of cards they bet and the determined by the number.