Simply put, the objective (usually, see Special Hands for exceptions) in mahjong is to make 4 sets of threes and a pair. The sets of three can be made in one of two ways: Chi or Pong. 

Players do this by taking turns to draw from the drawing pile and making a discard of an unwanted tile.  When a discard is claimed to form an exposed Chi or Pong, the player claiming the discard has to make a discard in turn (this is done without drawing from the drawing pile). 

Play always moves in a counter clockwise direction, based on which player made the last play.

A Chi is a numerically ascending sequence of three tiles (e.g. 1-2-3, 5-6-7, 7-8-9). For mahjong tiles, 1 is the smallest number and 9 the largest so 8-9-1 or 9-1-2 are NOT sequences).  It can be concealed or exposed.  A player can only claim the discard of the player to his/her immediate left to make an exposed Chi.  He/she does this by announcing “Chi” and exposing the other two tiles that make up the sequence. 

A Pong is a set of 3 similar tiles.  It can be concealed or exposed.  A player can claim the discard of any other player to make an exposed Pong.  He/she does this by announcing “Pong” and exposing the other two tiles that make up the Pong.

A Kong is a set of 4 similar tiles.  A Kong that is concealed is called an Um Kong.  Both Kong/Um Kong are worth points the moment they are exposed.  Since Kong/Um Kong involves 4 tiles, a replacement tile should be drawn from the flower pile, before making a discard.  Thus a player with an Um Kong should expose it and draw a replacement tile (else he/she will be a tile short to complete the rest of the hand), unless he/she intends to use the fourth tile as part of a Chow.

An exposed Kong can be made in one of two ways: (i) a player has a concealed Pong in hand and the fourth is discarded by another player or (ii) a player has an exposed Pong and he/she draws the fourth tile. 

Note that a Kong cannot be made by claiming the fourth tile from a discard to add to an exposed Pong.

Usually a pre-determined amount of points is assigned to each Kong/Um Kong since it potentially disrupts the scoring of a hand.

This occurs when a player’s hand is complete (i.e. it has 4 sets of three and a pair, has at least the minimum number of Doubles and fulfills any Special Hand requirements).

A claim to a discard to Hu supersedes any claim to Kong/Pong or Chi. 

A claim to a discard for Kong/Pong supersedes a claim for Chi.

If a discard results in Hu for 2 players, the player next in turn to the person who made the discard gets the claim (e.g. if South makes a discard that allows both North and East to Hu, North is the winner). 

This happens when one player makes a discard that allows all the other 3 players to Hu.  When this happens, all the players are considered to have won and the player making the discard loses the appropriate amount of points to each of the other players (e.g. East throws a tile that causes South (5 Doubles), West (3 Doubles) & North (4 Doubles) to Hu with 1 Double worth 10-20 points, East loses 640, 160 & 320 respectively). Not everyone plays this, so do check ahead of time.

When claiming a discard for Chi/Pong/Kong or Hu, it is advisable for the player to expose the other tiles forming the set first, before adding the discard to the set.  

The discard should not be placed in a player’s concealed tiles and then exposed as part of the Chi/Pong/Kong or Hu.  This is to prevent accusations of cheating or Zha Hu.

You should complete all necessary actions (i.e. taking in the discard to display with your exposed tiles) before your next opportunity to draw a tile.