The best knot site on the internet is Animated Knots. It has clear step-by-step animations of hundreds of knots.
Some basic useful knots are:
Hitches (to tie a rope to an object):
Clove hitch, using end and using loops
Round Turn and Two Half Hitches
Loops:
Bowline
Alpine Butterfly Loop
Bends (to join ropes):
Sheet bend
Reef knot
Stopper knots (to prevent a rope untwisting, or pulling through a hole):
Figure 8 (Flemish) Knot
Stevedore knot
It gets easier the more you practice. Each knot you learn will be easier than the last. Have fun!
Repeating the warning about the reef knot. It is absolutely not a bend! Heavy load or not. It is good for reefing and binding, securing your shoelaces, etc.
Taut line hitch is handy. Boy Scouts learn it so they can pitch a tent properly; this is the knot that lets you adjust the overall length of a line/loop manually, and have that length remain unchanged when tension is applied. Not just good for tents - decades later, I use it for bracing plants/trees in the yard, and occasionally for various projects that call for having a loop of rope that can be adjusted to just the right length after it’s been tied.
The bowline (for a fixed loop at the end of a line) and the bowline on a bight (fixed loop in the middle of a line) are musts. It’s used in rescues, climbing, or anyplace else that you need a nonslip knot.
A simple square knot is also essential; simple, but if you do it wrong you’ve got what’s called a ‘granny’ knot, which will slip or come undone.
Someone mentioned the sheet bend, which is great for joining two similar or dissimilar diameter ropes together. Again, nonslip if done right.
Ever tie stuff to the top of your car, then play hell keeping it from getting loose? Trucker’s hitch is the way to finish it off.
It’s a good knot for reefing/binding, just don’t use it as a bend
I am chiming back in to say that if you are closing up a bag, you can also use a slipped constrictor knot, that way you can get it open by pulling on the slipped end, without having to cut the knot.
This is my favorite knot that most people don’t know. I’ve used it any number of times for cinching down loads on top of my truck.
My first job out of college was as a field engineer for a steel construction company, mostly in the oil and gas industry. I was on one big job where we would have to lay out piping runs and their concrete supports; a taut piece of string is your friend here. So, one day when I was out with one other young engineer I tied one end of the string to a convenient bolt on a piece of equipment, and then 60 feet away or whatever it was I stuck a welding rod in the ground and tied a tautline hitch. Instant straight line. The guy I was working with acted like he’d just seen a miracle and made me teach him the knot right then and there.