1. I start with the two images which are already the same size. I happened to create these images with Cheezburger, but any images will work — just make sure they are the same height and width.
2. I start the GIMP and then to create the new file I choose the File-OpenAsLayers option. You can open multiple files at once, so I choose my two files and open both as layers. With just two images in the gif, it doesn't matter what order they are in, but for a more complex animation, you can arrange the order of the layers with the GIMP as needed.
3. Then I just do File-SaveAs and choose gif as the option. In the dialogue box that pops up about what to do with the layers, I choose "animation" and I usually set my animations to 2 seconds per frame (2000 milliseconds). That's it!
4. Click Export... and that's all! Isn't that simple??? I LOVE SIMPLE.
Writing up this tutorial has inspired me to go back through my GrammarCatz blog and turn them into animated gifs. I created the GrammarCatz as my own contribution to Common Core (mwahahaha), and I already have two cats for each graphic: one cat who meets Common Core English Language Arts Standards, and one cat who does not. Having the two graphics already done means it should be easy to make a new animated gif every day just for fun. Here is the Dude Cat: