Hopefully, if you are capable of reading this, you know how to tie your shoes. However, you probably don't know how to tie your shoes correctly, and you almost certainly have never seen the process demonstrated with ASCII art1.
The first method here is probably the most common method in use; there are other common ways, but they are nastier to draw, and still don't perform as well as the second method that I'll explain.
Anyway...
Typically, you start like this, with an untied show, the two laces hanging loose:
Lace 1 _____ _____ Lace 2
/ \ / \
/ _ \ / _ \
/ / \ \ / / \ \
| | | | | | | |
| | | | | | | |
\_/ | | | | \_/
| | | |
| | | |
Shoe
You then twist your laces around each other, like this:
______ ____ ____ _____
/ \/ \/ \/ \
\____ / / / ___/
\/ /\/ /\/ /
/ /\/ /\/ /\
/ / / / \
/ /\____/\____/\ \
/ / \ \
Now, you start with the more complicated stuff. With the first lace in one hand, you make a loop (labeled "A", in the diagram.) You then take the other lace (B), and wrap it around that loop.
______
/ \ A
/ _ \
/ / \ \
B | | | |
__________________| |___| |___
/ | | | | \
\__________________| |___| |_ \
| | | | \ \
______________|___|___|___|_/ /
/ /
/ ____________________________/
/ / G | | | |
| | ____ ____ | | | |
\ \/ \/ \/ / | |
\ / / / / | |
\/ /\/ /\/ / | |
/ /\/ /\/ /\ | |
/ / / / \ \_/
/ /\____/\____/\ \
/ / \ \
Then, you make a loop with the second lace (C), and pull it through the gap between the second lace itself, the first loop, and the twist, labelled "G", in the previous and next diagrams.
Finally, you pull on the two loops (A and B), until the knot tightens, and your shoe is tied.
_______
/ \ A
/ _ \
/ / \ \
| | | |
____| |___| |___
/ | | | | \
/ __| |___| |_ \
/ / | | | | \ \
______|___|___|___|___|___|_/ /
/ /
/ ____________________________/
/ / | | | | | |
| | \ \__|___|___|___|________
| | \ \
| | G \_______________________ \
B | | | | | | \ \ C
___________| |_____________|___|___|___|______/ /
/ | | /
\___________| |__________________________________/
| | | | | |
| | ____ ____ | | | |
\ \/ \/ \/ / | |
\ / / / / | |
\/ /\/ /\/ / | |
/ /\/ /\/ /\ | |
/ / / / \ \_/
/ /\____/\____/\ \
/ / \ \
Phew, wasn't that exciting? Well, if you have been tying your shoes like this for any amout of time, you have probably noticed that they tend to come undone pretty frequently, especially for thick laces that you find on work boots, hiking boots, or smooth laces that you find on dress shoes. If you are sick of having to constantly retie your shoelaces, or have resorted to double knoting them, then you will want to read on!
This second method starts the same way as the first, with the twist, but instead of immediately forming loops, you first pull each lace to the opposite side of the shoe, like this:
_____________
/ \
\___________ \
___________\___\________
/ \
/ ______________________/
/ / \ \
\ \ ____ ____ \ \
\ \/ \/ \/ /
\ / / / /
\/ /\/ /\/ /
/ /\/ /\/ /\
/ / / / \
/ /\____/\____/\ \
/ / \ \
The next diagram looks complicated, but the way you actually set it up is pretty simple. You make a loop with each loose end of the shoelace, and pull them through the space between the original twist, and the the crossed-over laces. Once you've done that, you just pull the loops tight, and you're done!
__
/ \
__ | | __
|\ ____ | | ____ /|
\ / \ \ \ / \ /
/ \ ____ _\__ \____ ____ / \
/ /\ \/ \/ \/ \/ \/ /\ \
/ / \ / / / / / / \ \
\ \ \/ /\/ /\/ /\/ /\/ / / /
\ \ / /\/ /\/ /\/ /\/ /\ / /
\ \/ / / / / / \/ /
\ / /\____/\____/\____/\____/\ / /
\/ / \ \____\/ /
/ / \ \ /\
/ / \ \_________/ \
/ / \ \__________________________\___\_______
\ \ \ \
\ \ \________________________________________/
\ \_______ ________/ /
\ \ ____ ____ / /
\_______ \/ \/ \/ ________/
\ / / / /
\/ /\/ /\/ /
/ /\/ /\/ /\
/ / / / \
/ /\____/\____/\ \
/ / \ \
The main difference between this knot and the more common ones, is that it has significantly more twists in it. More twists means more friction, and more friction means your laces are less likely to fall apart. (In the two or so years that I have been tying my shoes this way, my laces have come loose by themselves maybe ten times.)
Oh, you want to know how to untie your laces with this method? It's the same as always - just pull on both loose ends of your shoelace, and the knot will fall apart. You do have to apply slightly more tension than normal, but it isn't noticable, unless you are actually doing a side-by-side comparison test with the regular shoelace-tying method, to see how hard you have to pull to undo the knots.
So go forth, and let your shoelaces not become accidentally untied again!
1Thanks to tkil, from whom I blatantly stole the string-drawing style, as depicted in clove hitch.