"If you don't know knots, tie lots" is a lie. When was the last time you saw some idiot staggering around with eleven granny knots holding his tie in place, just because he never learned how to do a tie knot? At the very bare minimum, every self-respecting human being should be able to execute these five bits of cordage-wizadry. It's just common sense.
The bowline is a classic: first invented by sailors to attach ropes to sails, then claimed by climbers to tie themselves into ropes, it's the go-to knot for making a loop in a piece of rope.
The actual knot is pretty simple: as seen in the video above, make a loop of rope (with the working end on the bottom -- that's probably the most common mistake). Then, pass the working end through the loop, round the back of the rope, and back down through the loop. My favourite phrase for teaching the bowline (especially to small children) is "the rabbit goes up the hole (the hole being the loop), round the back of the tree, and back down the hole". Pro tip: practice tying the knot around your leg.
You should end up with a knot that looks like this:
If you need a more secure knot, you can make the tail end of the rope longer, then tie a Yosemite bowline.
But what if you want to tie two pieces of rope together, rather than onto something? In that case, the sheet bend is a pretty decent go-to. It's particularly great if you have to tie together two pieces of rope that aren't the same width.
The easiest way to think about the sheet bend is as forming a 'hook' with one piece of rope, then tying the other piece of rope up, through and round the hook. Your final product should look like the knot on the left. Particular point to note is that the two free ends should end up on the same side of the knot.
If you want maximum security, you can very simply turn a sheet bend into a double sheet bend: just wrap round the hook one more time!
So far, we've covered tying a rope around stuff (bowline), tying two bits of rope together (sheet bend), but what if you just want to tie your rope to something? The round turn and two half-hitches, whilst not elegantly named, is at least simple (and very self explanatory).
Simply wrap the rope a full turn around your handy pole (get yer mind out of the gutter), so that looking straight at the knot, you'll see the rope wrapping around twice, as it were. Then, pass the working end in front of the other strand, around the back, and through the little hole you've just created. Repeat, and you've got yourself a good solid knot that's easy to tie and untie under load (as opposed to a clove hitch or a bowline, which is pretty much impossible to untie under load).
If you want to make it a wee bit more secure, you can always opt for the fisherman's bend, which is almost identical, but less prone to become accidentally untied.
This is a knot you know, tied in a way you probably don't. The Fieggen shoelace is a way of tying a normal shoelace bow, but with fewer steps than the normal procedure.
Basically, tie the half-knot that you always start with, then form two loops, one facing each way. Pull the two strands nearest each other overtop, and tighten. The end result should look like a shoelace. Duh.
Great knot for anyone with a mass of cables, especially those that get tugged on in different directions (ahem, headphones). Essentially, it's a knot you can tie with two bits of cable coming from different directions, if you want to take the load off the actual ports/connections.
Tying it is simple. with one cable, make a loop, and pass the working end under the two strands of wire. With the other end, go around the other end, and through the hole you made before.