Rummy is a game that is usually played with 4 players, although you can also play it in 2 or 3 and there are even variations that allow up to 6 players to participate. You either play till a player reaches one target score or for a fixed amount of hands. Before the game starts there is a need that everyone agrees on winning conditions and game ending.
In most cases rummy games are played with cards, although you might also use tiles. In most variations a standard deck of 52 cards will be utilized. Rummy usually features a randomly chosen dealer that will deal alternatively or in a clockwise or anticlockwise motion if more than 2 players are playing, based on rummy game variations. The object of this game is to get rid of the cards that you have. This can be done once you make melding hands, lay-offs or discards. 
A melding is basically a combination of different cards that are placed in front of the player, on the playing table. 2 combination types are possible: sequences (more commonly known as runs) or sets (also related to as books or groups). A run is made out of a minimum of 3 cards of the same color and consecutive values. Sets are groups of a minimum of 3 cards of the exact same numeric value but different colors. A lay-off happens when you add one card or group of cards to hands that are already melded on the playing table. The result must be a valid new meld. You will discard a card on a discard pile at the end of one turn.
The winner of the game is decided in different ways, based on the rummy variation that you are playing. In most cases the first player to get rid of all cards will be the winner. Also, the scoring might be different from one game to the other. While in most cases the points of the cards are going to give you the point score value of your win and you can also get points when losing, there are also variations like Okey, in which only the winner is going to get points while the rest of the players receive penalties. We recommend that you look at the exact rules of the game or discuss them before playing so that no discussions appear.