The best/easiest way I know is to get yourself one of these...
-Run a piece of clear hose from it to your bleeder screw on the caliper
-Don't open the bleeder yet!
-Bleed the air out of the hose-don't wanna be pumping air into your system
-Open the bleeder screw and pump away...
-Keep an eye on the reservoir and you'll see the fluid level rise (obviously)
-Periodically soak the fluid out of the reservoir until you get all the old fluid out and you are full of clean,clear fluid.
Way easier than I made it sound.
Good luck,hope this helps!