Get yourself a glass container (an empty coffee jar works very well) and a length of hose (washer jet hose will do the job), pour some brake fluid into the glass container so the level is approx 1.5"-2" from the bottom, submerge one end of the hose in the brake fluid (ensure it's fully submerged and not likely to lift out) and push the other end over the bleed nipple on the caliper. Ensure the brake fluid master cylinder reservoir is top up, crack the bleed nipple off 1/2 a turn and then gentle depress the brake pedal. Make sure the pedal goes all the way to the floor and all the way back up again on each travel, do this 10-15 times and then recheck the fluid level in the reservoir. Once your done tighten the bleed nipple, top up the brake fluid and check the pedal feel.
If the pedal remains firm when your trying to bleed, tighten the bleed nipple and pump the brake pedal several times and then try the above process again. If you've got someone who can give you a hand then they can watch the glass container as you pump the pedal and tell you whether any more air can bee seen bleeding out.
