You can direct link to your file by providing a URL. This means you'll need to upload your image to an image host like Photobucket, Image Shack, or Imgur. Most of the time, you'll need to sign up for a free account, but Image Shack is an option if you don't want to do that. Do not direct link from websites like deviantART! Free image hosts are there for a reason! If you link to a picture from some place like deviantART or a personal website, you're stealing bandwidth, so do the right thing and use one of the free hosts!
Once you create an account and upload your image, you'll be given a URL, so you'll be able to go to your image.
Example:
http://img09.imageshack.us/img70/blahblah.png
You take your URL and put it into the text field in your avatar settings. You can do the same thing in your signature settings, or you can put the URL of your image in the forum's image tags (without the spaces, of course):
Example: [ img ]http://img09.imageshack.us/img70/blahblah.png[ /img ]