In your "User CP" (you can find it on the horizontal blue bar up top)

On the left part way down the menu is "Edit Avatar"

Click it.

There are two options. Ignore the first one...
The second one is "Upload an Avatar From Your Computer" with a browse button to the right. Click the browse button and find the picture, then select it.

THIS IS THE PART MOST PEOPLE MESS UP ON:

Once you have done all that, and the picture file is shown in the white box, click on:

SAVE CHANGES!!!

I'm not even a bit kidding - I forgot that a couple of times.

PS Dennis: That particular Avatar picture is exactly 60 X 60 and way under the max file size. I SET IT UP