It is a lot less complicated than some people assume but it is responsible for many a long debate.
Although the rule has been slightly altered numerous times over the past ten years the basic principle always applies.
Firstly a player is deemed offside only if he (I am not going to type he/she every time so for the purpose of this article let's assume the player is a he) is interfering with play when a player on the same team passes the ball forwards, he cannot be offside if the ball doesn't go forwards and also, he cannot be offside if he is in his own half when the ball is passed.
Basically the offside rule was created to stop players from goal hanging ie.
waiting at an opponents goal for the ball to arrive.
The distance the player is from the goal line relative to a defender on the other team is what determines whether he is offside.
The goal line is the line which runs from corner flag to corner flag through the opponents goalposts.
The essential offside rule is, if an attacking player, when the ball is passed forwards by one of his team mates, is closer than all but one defending player, usually the goalkeeper but not necessarily, to the goal line, he is deemed to be offside.
The rule has varied over the years but that is basically it and if you can grasp that simple concept you can join in next time you hear an offside debate.