The basic rule is that when you play the ball forward, there have to be at least two opposition players between your most advanced team-mate and the goal line. A player can’t be offside in his own half of the pitch though, and you can’t be offside from a throw-in.

In practice, the goalkeeper is almost always one of the two opposition players, so you’re normally looking at whether there is a defender between your most advanced team-mate and the goal line.

The purpose of the rule is to prevent goal hanging and compress the play into a smaller area (if you watch a match in person having normally watched on TV, it’s surprising to see how small an area of the pitch almost all the players are in). The game is what it is today pretty much because of the offside rule.

There’s also various additional details that are important in practice (e.g. is the offside player “active”, what part of his body counts as being offside, what phase of play are you in etc.) but they’re all fiddling around the edges of the basic rule.