By far, the knots I use the most are the square knot, the lark's head, and maybe the half hitch. There are some other nice ones but they're not essential. There are lots of websites out there with knot diagrams. Square knot - Really good for tying two ends together. When I'm tying it, I think "left over right, then right over left."
Granny knot - It's usually best to avoid the granny knot. Basically it's a poorly tied version of the square knot. When tying, if you go "left over right, then "left over right" again, you'll end up with a granny knot. It's not as secure as the square knot, can slip fairly easily and it tends to twist over on itself.
Larks head - I pretty much always start out with a lark's head. You just double up a rope to form a loop, go around the ankles, for example, run the ends through the loop and tighten down - a good start.
Half hitch and double half hitch - good for tying a rope off to an inanimate object. If you only make one loop it's a half hitch; two loops as in the picture, and it's a double half hitch.
Clove hitch - also really nice for tying off a rope to an inanimate object.
Figure-eight - simple knot for finishing off an end, for example, to prevent unraveling.
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