If you're cheap (like me) you can do this without the alligator clips.
Just take any wire - I used a phone cord - strip the ends and attach one end to the computer case (back a screw off, wrap the bare wire around the screw and re-tighten it) and the other end to the outside of the BNC connector of the antenna. For that I just unscrewed the antenna, wrapped the bare wire around the outside of the 'post', and reattached the antenna. Just be careful to make sure your wire is only in contact with the outside of the antenna and not the center bit.