Hi CM!
vBulletin is a really neat forum software, it's really one of the best out there. Navigating it can be difficult for those who aren't familiar, however. Hopefully I can help you out.
I assume you have a picture in mind to use, and that you already have it saved to your computer. You'll need to get it hosted on the internet somewhere, and I highly recommend using
http://www.imgur.com if you need a host; it's free and easy to use, just navigate there and click on "Computer" in the upper right hand corner of their front page, you'll be able to browse your computer for the file in question. Once it's uploaded, it will give you a URL to use. Assuming you don't already have it uploaded somewhere!
Next, you'll want to click on "User CP" in the upper left-hand corner of the forum. Any page on the forum will have it available at the top of the screen, so long as you're logged in. This will bring you to the User Control Panel, with a number of options along the left-hand side of the screen. One of the options is "Edit Avatar" which brings you to a page for either uploading or linking to your image. I suggest linking to off-site avatars, but you can also use the forum as a host for your image; you won't be able to upload a picture for your signature in the same way. There are certain limitations on the size and dimensions of your avatar, but I can help you resize a gif if it does not go through.
User CP location -
https://dl.dropboxusercontent.com/u/.../graalians.PNG
Edit Avatar location -
https://dl.dropboxusercontent.com/u/...graalians2.png
Edit Avatar screen -
https://dl.dropboxusercontent.com/u/...graalians3.PNG
You'll probably notice the Edit Signature area, as well. This area is a bit more confusing for those who are not familiar with HTML editing, or BBCode. It should have a WYSIWYG (what you see is what you get) rich editor that will allow you to insert an image. This forum, like many, has strict rules on how large your signature can be so... don't go too nuts!