The program I use is Photoshop. (You can download a free trial here: http://www.photoshop.com/) and once you’ve downloaded the trial I can help you on how to make the gifs.
There are also free sites (http://makeagif.com/) that allow you to upload image sequences to make gifs, but you can’t edit them and “make them pretty” like you could in Photoshop and the frames don’t run as smoothly.
Hope this helps! Let me know if you have any other questions :)