Assisting is a technique used to concentrate firepower on single targets to kill them more quickly, while simultaneously protecting non-tanks from pulling aggro.
Typically party members are expected to follow one particular player and select his target. This character is normally known as the main assist, or MA. If that player is not specifically designated, usually it is best to follow the main tank. This is a crucial party skill because it becomes much easier to manage a battle with 2 targets rather than 4 half-dead enemies. Additionally, the tank will probably not be able to maintain hate over the people damaging these different opponents, and they will be attacked themselves, meaning they will take more damage and strain healer mana or possibly die.
There are several different ways to assist another player. For these examples, Leeroy is the name of the player you are trying to assist.
Option #4 is usually the preferred method, as it requires a single button push.