Get the offside call right
The most important and potentially controversial role of the linesman is to get the offside call right. It is difficult. This video shows exactly how difficult it is.
The key thing is to; Stay level with the last defender.
Try to adjust for the movement that occurred between the pass and when the line was checked (this is where mistakes are made).
The Offside Rule
If you are not sure about the offside rule. Check out this little video.
Linesman Signals
This video looks at the signals a linesman might need to know.
The key thing is raise the flag when you need to get the referees attention, and point it in the direction that the team who gets the ball is attacking.
It might be worth asking the ref at the start of the game, exactly what he wants you to flag. He may only want you to do offside, and whose ball is it if the ball goes out of play.