I've scarcely scratched the surface of its features, but I was able to be up and running with tessellation in a short time. Here are the steps I follow:

1. open a jpg in GIMP (<control><o>)
2. COPY the image (<control><c>)
3. open a new GIMP window (<control><n>)
4. PASTE clipboard into new window (<control><v>)
5. IMAGE > TRANSFORM > FLIP horizontal or vertical
6. COPY the image (<control><c>)
7. back to original image and IMAGE > CANVAS size and set to be 2x the height or width of the value shown
8. EDIT > PASTE AS > New Layer
9. use the Move tool to position the newly-added layer, matching carefully
10. IMAGE > FIT CANVAS to layers
11. IMAGE > FLATTEN Image
12. SAVE AS with a new name

    ...and repeat as desired