This maybe the world's most simple, compact and inexpensive GoPro stabilizer. ;-)
Print out the two parts of the stabilizer, the GoPro clip/tripot mount and the finger ring. For strength, print using at least 3 perimeter, 3 solid top and bottom, and 30% fill. Print with support.
Clean the hole in the mount with a 7/32"dia. drill and thread the hole with a 1/4-20 tap; or just slowly and carefully run a 1/4-20 bolt through it a few times.
Assemble the two part with strong adhesive; a good two part epoxy works well.
Get yourself a compact telescopic monopod. Here is the one that I use, about $10. You can get one from here: http://dx.com/p/stainless-steel-handheld-monopod-for-digital-camera-42504
Attach your GoPro and a monopod to the stabilizer as shown in the pictures.
Hook you finger through the ring and try to balance the GoPro for best stability; by rotating the joints on the GoPro mount, tripod mount, and extending the monopod handle.
There are tons of "Steadicam" balancing and operational videos on Youtube. The same general principles apply.