What I learned in college is that if you grab a bag load of screenshots, place them in order on a program designed to follow the pictures in an order and capable of editing and designing beside it, then you are guaranteed your GIF.
Personally I would use Adobe Flash Player which is sometimes used in class to design video GIFs.
By doing this, you simply go into the timeline and post the pictures in the movement order, play the GIF to make sure it's all in order, make edits and then save as a GIF file.
So:
1. Post pictures in order on the timeline.
2. Play the order to check it's correct.
3. Make edits. (Optional)
4. Save as a GIF file format.
Someone do correct me if i'm wrong. ~Sibby.