The first one was Alchemy's GIF animator program. Shareware that cost like $15 at the time. Moved up to Jasc Paint Shop Pro and Animation Shop. They were also shareware, but don't recall how much they cost. They gave Photoshop such a fun for the money that they were bought out by them.
If you understand the basic principle of animation, you've got a good start. Do you remember flipbooks in school. Fan the pages and a drawing would appear to move? Same principle. With GIFs, though, you start with a background layer, out the item you're going to animate on a new layer. Copy that item to a new layer and do your movements. There's a lot more and I'm not set up to do it here. Only have cell phone access. Each layer shows some movement. Biggest animated GIF I ever made was about 400 frames. Took me 4 hours,, but the pay was good. Some I did for fun were 70 or 80 frames.
