When I tutor, I either really like to use the explanations from Maria Miller (Click Fact Sheet 2 at the right of this page..
To help them remember, I tell a goofy story my Algebra teacher told us in the dark ages--but you have to really ham it up!
Two bad guys from the Old West (negative signs in black cowboy hats) meet up. They shoot each other and both die. Everybody's happy. Yay! So, two negatives meeting up gives you a positive result. The rest of the story explains - X +; She just said that the bad guys were reallly strong and always won in this town.