These are available in 2 sizes-- 7/8" long and 2" long. To use either size you simply hammer them into the wood of your base. (My inclination would be to do this before applying the mosaic if your base is 1/4" thick.)
I recently got these in for a customer and have not used them myself. I'll update this listing when I have.
The reviews I have read show these to be very sturdy. Apparently the 2" hangers will hold a wine rack and 6 bottles of wine, so they should work well with most mosaic wall art.