If you can put a rubber hose on the bleeder screw,put the other end into a container with brake fluid in it(making sure it doesn't come out of the fluid).When you pump the brake it will bubble.When the bubbling stops,there's no more air in the lines.Make sure you check the fluid in the master cylinder(you DON'T want it to empty).I use this system when I do the brakes on my motorbike.
Does anybody know of a quick way to bleed this system?
Did you want to know the quick way or the correct way?
Quick way: Find the reservoir, top it off (with the correct fluid, see below) then ride.
Correct way: Read the manual that came with the bike, bleed according to the manufacturer's instructions.
Unfortunately the Quad brand is an OEM product for the most part and service info seems to be a bit scarce. The basic process posted by raleighrider75 is correct, but systems do vary, usually in the fittings they require. Other than that, an irrigation syringe and something to catch the fluid is all that is typically needed.
About fluid: Make sure to use the correct fluid. It will either be mineral oil or a DOT fluid. Never use one in a system made for the other or you risk dissolving all the seals.