There is a lot of information in the Tech section on bleeding brakes.
Easiest way I have found with a totally dry system or otherwise: If you have rebuilt the caliper, you want the piston pushed all the way in on install. Less air to bleed out.
With everything hooked up, the MC needs to be level or slightly nose down on the hose end. Sometimes you can just turn the bars.
-Fill the Resv. about 1/2 full.
-Open the bleeder a good turn on the caliper, until you see fluid running out. Close it. Bleeder is on the top. Just wait for the fluid. May take a bit.
- The air in the system will rise to the top and into the MC but... Don't just pull the brake lever all the way in and don't pump it.
- Pull the brake lever just the slightest amount working the piston. If the lever adjustment is close, about 1/4 inch or less lever movement is all you want. The object is to allow the air bubbles in the line to come to the top and exit the MC thru the port. You will at first see a lot of big bubbles.
- When the bubbles get smaller, pull the brake lever fully in and let it out, slowly! Keep an eye on the fluid level in the Resv.
- The bubbles need help to exit the MC port. You will see a bubble just sitting at the top of the port. Using a zip tie, touch the bubble and it will let go and rise. No tapping needed. Don't stick anything down into the port, like a tooth pick! Keep the zip tie in the top of the hole and return to slightly moving the piston. Your working with the air in the very top of the system, around the piston, and allowing fluid to replace the air in the lower part that is rising to where your working.
Helping the bubbles to escape using the zip tie is really important.
- After a time it seems like there are no more bubbles. Pull in on the lever and let it out, slowly. You should feel a brake. Don't worry about the sponge. You should see a trail of small bubbles that may need help. Soon, as you pull the lever firmly and release, you will see a fog. You should have a good brake at this point. The fog is a sure sign very little air is left in the system. Usually the system will purge the remaining air on it's own.
It's not hard and not messy.
Just be sure to not let the MC resv. run dry while working, and easy on the lever. You don't what to force any air in the piston area, into the top of the brake line any further than it takes to work the piston a bit.
What do the steady pulls do? When it's time for the first pull, enough of the air should be out of the system to allow the filled caliper to push out against the rotor. Your not looking for a hard brake at this point, but if your close to getting one, so much the better. The second and later pulls are to put pressure on remaining air. It will show as small bubbles or fog.
Leave the system to set a bit and then check again for fog.