DRS (Drag Reduction System) refers to the movable rear wing. In qualifying, you may use DRS as often as you like for an increase in straight line speed. In races, you need to be within a one second gap (to the next driver) when crossing designated points on the tracks. The DRS zone is a white line, going horizontally across the track. If you're within the one second gap when you cross the line, you will see the DRS button in the bottom right corner turn green. This means you can use it. Activate it by pressing and cleanly overtake another car. There is an audible click when you activate it and you will see the DRS button flash. If you brake or press again, DRS will deactivate.
Most circuits have one DRS zone, but a couple, such as Montreal and Monza have two. Be careful when using DRS (especially in qualifying) as you will have severely reduced downforce and thus less grip. Straights are fine. Also, DRS is disabled in the first two laps of a Grand Prix, for two laps after a safety car/restart and completely disabled if the race is wet.
An example of a DRS zone is shown below (Australia):