Continuing the discussion from Category definition for Support:
The Upload button triggers a hidden
<input type="file"> element which should trigger your browser's built in file selection dialog box.
If nothing happens when you click it then I suggest you try another browser.
Uploading Custom Avatar: Nothing happens after upload
After uploading a custom avatar you will still be at the Change your avatar box and your previous (or blank) avatar will still be shown. There is no message that the new avatar has been successfully uploaded and set.
Click Save Changes and then refresh the page and you will see your new avatar.