Internet 101 good friend. Welcome to the web.
My personal recommendations for image hosting are
minus (Other popular alternatives are imagur, puush, photobucket, imageshack, etc) I prefer minus because it gives a lot of space, holds things other than just images, has a pretty good interface, and is like never down.
If you have the gif file on your computer, you must first upload it to the internet. Either of these two sites will let you do it. If it is already on the internet, then you should get a url link to it. The simplest way to hotlink a url from an image is to right click it, and select "Copy Image URL" which should put the image link on your clipboard.
Then you paste it between image tags for bbc.
[Image: image-link-here]
So it should look kinda like this
[ img]http://www.website.com/picture.gif[/img]
Paste that link into your signature box in the settings for mabination and you're good to go!