The figure eight is used primarily as a stopper knot which means it will give you a big nob so it won't pull through a pulley. It is also found in fancy work. It is easy to untie even after being put under tremendous pressure. A variation is sometimes used by climbers as a 'tie in' for attaching a climbing rope to a harness.
Begin by taking a round turn with the bitter end coming over the standing part.
Forming an "S" put the bitter under the standing part.
Push the bitter down through the first round turn you made.
Finish by drawing it snug.
This knot can also be used to join two ropes together, either of equal size or not. However, for all practical purposes the sheet bend is more suited to this purpose. There are several variations for other applications. To see some of them go to Figure Eight Variations.