First of all, you need to get a copy of the show you want to make a GIF from on your computer. I can't tell you how to do this, but try finding another guide that describes how to rip a DVD into an AVI.
Next, you need a program that will allow you to take screenshots from a movie file. There are many programs that do this. The one I'm using is a free program called "Movie Snapshot," which is available here:
http://www.cd2html.de/moviesnapshot.en.htmlUPDATE: Another program I would reccomend for this task is VirtualDubMod. It's less simple, and a little more daunting than Movie Snapshot, but I also find it to be a little more stable and compatible with opening movie files. It also has many more features than Movie Snapshot. You can get it here:
http://virtualdubmod.sourceforge.net/Last, you need the GIMP, a free Image editing program, which you can get from this website:
http://gimp-win.sourceforge.net/