Steps:
1. Know that there are many types of brakes. Some are easier to adjust than others. Road bike side-pull brakes are fairly simple to adjust; cantilever brakes are much more complicated.
2. Determine what is causing your braking problem. Is it a loose or damaged cable? Are the pads worn? Is the rim damaged or greasy?
3. Adjust the cable tension if needed. This can often be done easily with a barrel adjuster found on the brake lever. Sometimes there's a second barrel adjuster located on the front cable hanger or on the brake itself.
4. Reposition the brake pads if needed. As brake pads wear, they'll often start to dive under the rim. You may need to raise them, and you may even need to remove them and file them down so that they're smooth. Again, on cantilever brakes, adjustment is somewhat tricky (it's done with a 5mm Allen wrench and an open 10mm wrench), so you may want to take the bike to a qualified mechanic.
5. Adjust the brake pad toe-in: The front part of the brake pad needs to make contact with the rim before the back part of the pad does. This prevents the pad from squealing.
6. Center the brakes if needed. In many cases, this can be done by adjusting the spring tension - generally a small set screw on the brake itself. On side-pulls, you may need to loosen the center bolt that attaches the brake to the frame.
7. Know that many bike mechanics consider adjusting brakes to be a fine art. Getting them just right can be fairly difficult.
Tips:
Clean wheel rims with a pure alcohol solution. In some cases, you may need to use a scouring pad to remove the built-up brake pad residue.
Warnings:
If you feel unsure of your brake repair skills, have this done by a qualified mechanic - poorly adjusted brakes increase your chance of injury.