Here's how I bleed brakes when a really complete bleed is required:

1. Go around and tap on everything brake related, to jar bubbles loose.
2. Make sure all of the bleeder screws will loosen okay and that there is a visible amount of fluid released from each when you loosen them slightly. If not, remove those that are clogged and clear the bleed hole with a piece of wire or small drill-bit.
3. Use the method of bleeding where you press a medium length of clear plastic tubing onto the bleed nipple and put the other end under the surface of a small amount of brake fluid in an old bottle. Pump the brake, nice slow full strokes, until there are no visible bubbles coming through the tubing. Don't run the master cylinder dry; keep it at least half full.
4. It's worthwhile to do this for all four wheels, then tap everything with the small hammer again: calipers, drum backing plates, lines, junctions, switch housing, master cylinder, etc.
5. Assuming that by this time there is nothing in the system but new, clean fluid (don't do this next step unless the fluid is clean), I then run a looooong piece of the tubing from each bleed nipple in turn into the master cylinder reservoir and then continually pump the brake pedal and watch the plastic tubing for particulate contaminants (if they appear, I take the end of the tube out of the reservoir and direct the contaminant into a waste fluid bottle; same thing for any discoloration. Since there is no necessity to keep the MC reservoir full, you can really circulate the fluid; the bubbles will float to the top of the reservoir and therefore be removed from the circuit. Once there are no more tiny bubbles in the line (wow, sounds like a song title there), close off the bleeder screw.

Once all four wheels have been done, then I apply pressure onto the brake pedal, using a piece of wood as a prop or something similar and then leave it overnight.

So far this has always worked for me.

CAVEAT: Drum brakes should be adjusted *before* doing this procedure.

-Rock http://www.rocky-frisco.com

Additional notes by Skye:

1. You can make a one-way valve for the end of your tubing very easily with a plastic sandwich bag. Just attach it to the end of the hose with a rubber band, and cut the tip of a corner off. When fluid tries to go back up the hose, the bag will collapse and cut off the return path. Change your "valve" often as the material will degrade from contact with the fluid.
2. I believe you need 13 ft of tubing to reach from the furthest bleed nipple back to the MC.