I use a combination of software applications.
There is
The Gimp, which is free and quite easy. You can't edit existing gif frames though. But you can do that in
Easy Gif Animator, which is dirt cheap - about 15 euros.
So, create a gif in
Gimp and use
Easy Gif to edit frames in conjunction with
Paint Shop or similar.
Sounds complicated but it isn't. Trust me. If I can do it, anyone can.