If your mosaic fits perfectly into a pre-made frame, lucky you! If you make your own frames, more lucky you. In many cases, though, the mosaic either doesn't fit into a conventional frame (like thick MDF) or you've forgotten to add hanging hardware to the back of the original mosaic.
Here, thanks to photos from a student, is a quick illustration of how to use mirror clips. CLICK on the image or hold your mouse over it to see the comments.
There are many ways to frame a mosaic. I usually recommend you consider how you are going to frame it BEFORE you create the mosaic, but hey, it doesn't always happen that way, does it?
I create mosaics by using reclaimed, recycled, and re-purposed materials.