How can you get air bubbles out of the brake system for a 1995 Toyota Corolla?

Google your question and it should take you to a site that will show you step by step on how to bleed brakes.

Keep bleeding the brakes until the pedal is firm and all air bubbles are gone. Sometimes it takes several bleeds.

Sometimes pushing the pedal to the floor will ruin the master cylinder. I always put a short 2x4 or similar under the brake pedal to keep it from going to the floor. Power bleeding brakes is best.

Begin at R/R (passenger side rear, furthest from master cylinder) then L/R, R/F last L/F. You need a helper to step on brake pedal and while there is pressure on pedal -- open bleeder valve, allow some fluid and air out. CLOSE BLEEDER VALVE BEFORE PEDAL GOES ALL THE WAY TO FLOOR. You must maintain communication between person stepping on pedal to know. The person stepping on pedal can shout "NOW" to warn you pedal is getting low. Keep topping off master cylinder, do not allow it to begin to draw air, i.e. keep full. Go around as many times as necessary. Use a hose and a jar if you choose to, to collect waste fluid..or a piece of cardboard on floor will do.

Bob is right. I was off looking for an image Proceed with engine running is what he means (I think)

Power bleeding is using a pressurized apparatus to force fluid through the system.

http://www.motiveproducts.com/

Ah..of course. Should not assume.

LOOSEN THE BLEEDING SCREW ATTACH A PIPE THAT LEADS INTO A SEE THRU BOTTLE FULLED HALF WAY WITH BRAKE FLUID, PUMP THE BRAKE UNTIL BUBBLES IS GONE TIGHTEN AND YOUR DONE AFTER YOU'VE DONE ALL 4