Tooth bleaching is a way to lighten teeth without bonding material to the teeth, or removing any sound tooth structure. In this respect, it's one of the most conservative cosmetic procedures. It's an "old" procedure, back in vogue.
First, the tooth is isolated with a rubber dam. This protects your gums and tongue, too. Then the tooth is cleaned thoroughly. Your tooth may or may not be pre-conditioned to help the teeth whitening products penetrate.
The tooth is covered with gauze, and the teeth bleaching solution is carefully applied. A heat source "cures" the bleach and hastens the process. These steps are repeated several times, depending on the appropriate level of whiteness you want to achieve. The color of adjacent teeth will be considered too, so you'll look natural (there is such a thing as too white).
A professional tooth whitening session takes 30 to 45 minutes - and there you are. After three to five sessions, the tooth really shows the difference.
The success of the procedure depends in part on what caused the tooth staining in the first place. Surface coffee, tea, and tobacco stains that resist cleaning can be bleached away (the stains will reappear over time if you continue to indulge, of course). Antibiotic staining - from tetracycline, for example - is a bit harder to treat with simple teeth bleaching. Alternatively, a jacket or porcelain veneers may be called for. The idea is to be very selective about which tooth is a good candidate for the procedure.