This short video shows one how to tie the figure-eight follow-through. The climber in the video does a great job of dressing the knot. In other words she doesn't have any weird crosses and the knot looks very clean. What she does a poor job with is her "back-up" knot. If you use one, it should be a strangle knot, also commonly referred to as a single fisherman's knot or a barrel knot.
This second video shows the proper finish, but names it improperly. They call it a double fisherman's knot in this video, when it is actually a strangle knot.
The reality of the so-called "back-up knot" is that it is not necessary. If your knot is dressed and there is at least one fist worth of rope sticking out of the end of the knot, then all will be well.
If -- for some reason -- one strand of the figure-eight follow-through becomes unwoven, the knot still has a tremendous amount of holding power. Indeed, the lack of the final follow-through changes the knot from a figure-eight follow-through to an in-line or directional figure eight. While certainly not a preferred climbing knot, it will easily hold body weight.
The fact that the knot is still effective if the final strand becomes unwoven is essentially a back-up in and of itself. This means that the use of a strangle knot (barrel knot/single fisherman's) behind a figure-eight follow-through is a waste of rope.
Many of my students tell me that after they related this information about back-up knots to the manager of their climbing gym, the manager wouldn't relent on his gym's back-up knot policy. This is not something to sweat over. If your gym requires that you tie such a knot, you should just do it. Some gyms have insurance policies that require this unnecessary step, whereas others have created protocol based systems that are hard to change without chopping through a lot of red tape. It is less of a headache if you just follow the gym's rules while you are there.
Some climbers like to finish their figure-eight with a "Yosemite tuck" or "Yosemite finish." This common technique is accomplished by tucking the end of the rope back into the knot. The upside of this is that it can clean up the knot. The downside is that this technique may seriously weaken the knot, if you use the inside of the knot as a belay loop. If you load the loop of the knot, it is possible that it will invert, after which you will only have part of the figure-eight remaining. Some people cure this problem by passing the rope around itself before going through the hole, but that makes the knot a little bigger.
And lastly, this is a nice video that shows an overview of a few different figure-eight knots from the figure-eight family:
--Jason D. Martin