At the top of the web page (above Dartmoor Geocaching) there is another menu. On the left you should see your Username, next to this there should be a Dashboard entry. Everybody has the same privileges, so you can all perform the same actions. On both of these menus there is Profile option. Select that and you can change your password, etc. At the bottom of the profile options it says Avatar and there you have the option to upload a new avatar. Several members (including myself) have changed their avatar so I know it works.
I can confirm it the instructions that Dave has given do work, just remember to click the “update profile” button to make the changes take effect. I didnt scroll down the page far enough and didnt see the button the first time and wondered why the avatar wouldnt change.