This procedure will work great if there are no mechanical problems in your brake system. Bleeding brakes WILL NOT repair mechanical damage!!! For example if your master cylinder or a wheel cylinder is bad you can bleed the brakes all day long and your brakes will still not work, or will not work correctly.
There are several ways to do this job - one involves 2 people, one pumping the brake pedal and the other opening and closing the respective bleeder valve at each wheel. This method is great for Father/Son/Daughter quality time but doesn't actually work very reliably for bleeding the brakes unless you have lots of practice. The reason is that if anybody makes a mistake in the execution of this "dance" it introduces air back into the system and you need to start over. The other problem with this system is that it takes 2 people, sometimes a luxury we don't have.
The first thing is that if you have changed the master cylinder it needs to be bled separately. Buy one of the $3 master cylinder bleeder kits from the auto parts store, or take an old brake line and bend it around so the end goes back into the fluid reservoir on top. You need 2 lines on a dual master cylinder. Fill the cylinder's reservoir and clamp the flange in the vice on your bench. Using a large Philips screwdriver pump the cylinder until all the air is gone from the brake fluid. It helps to stop every few pumps and let the air rise out of the reservoir. You can do this same job with it mounted in the car but it makes a mess and is more complicated if you have power brakes.
The one real "trick" is to build and use a catch bottle at the wheel end of the system. I use a 1 liter plastic pop bottle with a 1/4" hole drilled through the cap. Then you will need about a 2 feet long piece of 1/4" clear surgical rubber tubing. Push the tubing through the hole in the cap and all the way down to the bottom of the bottle. Then fill the bottle about 1/4 of the way up with brake fluid.
You will have a lot better success on a car with power brakes if you start the engine and just let it idle. Some cars will pump just fine without the power assist, others will just never bleed out. Better safe then sorry, start the car. On non power systems it makes no difference, leave it shut off.
Go to the right side rear wheel of the car and open the bleeder valve about 1 turn. Push the end of the tube onto the tapered end of the bleeder valve and make sure the bottle is supported on something solid. Make sure the tube is immersed in the brake fluid in the bottom of the bottle. With the master cylinder full go inside and pump the pedal no more then 5 times and check the master cylinder level again. You want to be careful not to run the reservoir out of fluid or you will have to start over again. Top it off when necessary during this process. Now pump it about 5 more times and check it again. Repeat, repeat repeat. Check the bottle about every 10 pumps for getting too full.
At this point what you want to look for is bubbles/air in the hose going to the bottle. Once you reach the point that you are not getting any more bubbles then there is no more air in that line. Always close the bleeder before you remove the hose, that way no new air has a chance to get into the system.
Then move on to the left rear, the right front, and the left front.
If you follow this procedure you will have done a proper brake bleeding job and will have no air left in the system. I hope this helps save you a lot of hassles.