This article will give you a jump start about usefull knots when paddling. I attempted to show them step by step so they are easy to follow.

Bow Line

An easy way to remember this knot is by using a figure of a frog.

Start by creating an overhand loop and bring the free end around the obstacle you want to fix your rope to.

-frog: make a pond (an overhand loop is a pond, it won't fall open, an underhand loop is not a pond, it will run empty when you loose it.

Put the loose end of your knot from underneath in the loop

frog: put the frog in the pond

Loop the free end around the fixed end of your rope and slide it back into the overhand loop.
frog: the fixed and is a tree; the frog jumps out of the pond, runs around the tree and jumps back in the pond

take the parallel ends of the free end and the loop together, but pull on the fixed and to tighten your knot.
frog: grab the frog, but pull on the tree, you don't like frog-legs.

Figure-8

The figure-8 knot is a strong knot, easily to untie after tension and very reliable. The next 2 images illustrate how to make such a knot:

Here you make an overhand loop with the free end.

 Next you lead the free end under the fixed end, and with the free end through the overhand loop you created in the previous step.

Pull both ends to tighten.

Figure-8 bowline alternative

This knot is a very interesting alternative to the bow-line knot. The bow line knot always leaves room for obstacles to get caught in the loop you create there.
This knot is a figure-8 knot around the long end of the rope, allowing you to slip the knot and thus having no loops left in your bowline.

Watch the following images:

The start is the same 

Watch the overhand loop, and notice the fixed end of the line is going through the overhand loop. 

Finish your figure-8 knot 

tighten your knot.
Notice the loop you've just created, that's the loop you can slip. But of course you should have made sure your rope was going around the obstacle.

Something like this 

And then slip the knot by pulling the long end:

Truckers Hitch

This is a very useful and simple knot to fix something with a rope that needs tension.

Let's have a look.

You start with a free end, creating an overhand loop with the free end, and make a rope "bulb" from underhand with the free end (left side is the free end)

Creating the "bulb"

Tighten the bulb

Gide the free end around a fixed obstacle you can use to create the tension. Then loop the free end through the newly created bulb, and pull back to the obstacle.

Finish your truckers hitch with a knot you prefer. Either close to the bulb, or by winding half around the obstacle, and then winding around the 2 rope ends that go to the bulb, putting some extra tension on the rope.