Playing Mahjong
Every player attempts to form a what is considered a "legal set" from the tiles in their hand by drawing a new tile and discarding an old one each turn. A set consists of different groups of cards called Chows, Pungs and Kongs. A Chow is three sequential cards of the same suit. A Pung is three of the same tiles from the same suit. A Kong is four same-suited identical tiles. A combination of four Chows, Pungs, and Kongs, as well as a set of two identical cards, adding up to 14 tiles in all, is a winning Mahjong set.
At the beginning of the game, each player is dealt 13 tiles that make up a hand. A 14th tile is given to each player at the beginning of his turn. The player can decide to discard the dealt tile, and it will go into the middle. If he keeps it, he must discard a different tile instead. When any player can use the discarded tile to make a Pung or Kong, he may call out the respective word and claim it. If the player to the left discards a tile that will let you make a Chow, you may claim it by calling out "Chow." All made combinations like this are laid out face up in front of the player.
Strategies
Two things to keep in mind are the winds and seasons. Each of the four players is assigned a specific wind and season. If you can collect or Pung or Kong of your own wind or season, it will be worth much more than a comparable group from another player's wind or season.
When scoring mahjong, exposed groups are worth only half as much as concealed groups. For that reason, going for a Pung from a discarded tile is worth little, and, while a gamble, attempting to draw the card yourself could pay out for you later, with double the value.
If you're memory is good, you can try to keep in mind what tiles have been discarded by your opponents. In doing this you can approximate which suits and numbers may be of no use to the other players and prevent handing them a card they needed for a group when you discard it.