Making .gif files

We want to make a small animated (duh!) gif file for on our website.
Visitors would click on it to be taken to another web page.

We have never done anything like that before. What I know about gifs is
this: It's a series of pictures flashed up in series, that tricks our eyes
into thinking it's movement. Like a film.

Looking to make a semi truck with it's wheels spinning, or a banner where
the truck moves across part of the page. We don't want it too flashy,
though, such that it irritates people. Want to put some verbiage on the
side of the truck.

Is this something a small company like us could come up with ourselves?
Software suggestions?

Thanks.