Click on your User CP.
Click on Edit Avatar.
Scroll down. Here you will see two options. The top one will have "Enter avatar URL" over a blank space.
You do not want this option if you are uploading.
You want the second space which says, " Upload an Avatar From Your Computer". Beside the white space it will have a small grey button that says "Browse." Click that button.
When you push that, it will open a window with all of the documents, files, and pictures in it. From here on out, it's just like selecting and navigating in My Pictures. So, go to my Pictures, click a picture that is within the 64 by 64 pixels limitations, and double click. THe window will disappear and the file name will appear in the white box.
Push save changes.
Voile. Avatar.