It has become an axiom worth remembering that, whatever you want to know more about, you can probably find a page about it on the Internet.
So it is with shoelace knots. Ian Fieggen has built a tremendous repository of information about shoelaces, especially the tying thereof.
If you take any single thing away from this site, it should be the Ian Knot, a faster way to do the usual shoelace knot. The animated GIF in the top-left of that page shows how quickly the knot ties. Fieggen has a video that shows the process in detail, and another user uploaded to YouTube another, shorter video that Fieggen made several years ago that shows the knot from the wearer’s angle.
Also worth checking out is his article on the granny knot, which is when you tie your shoes incorrectly and they won’t stay tied. He explains the problem and offers a very simple way to correct it.