Adhesive is one of the most important materials needed to create a well crafted mosaic. Stay away from inexpensive water-based glues like Elmers and Elmers "Glue All" Craft glue. Glues like that are so weak that when you apply grout, the moisture from the grout will cause the glue to breakdown and your glass will fall out as you are scraping and sponging your excess grout. Also stay away from novelty adhesives that you will find at craft and art supply stores. These adhesives are usually called simply "mosaic adhesive" or "Mosaic Grout and Adhesive". They dry too fast and you'll end wasting more glue that actually using it. This can cause an uneven-surfaced mosaic. They also tend to be white in color, which is okay if you have opaque or solid colored glass but if you want to use translucent glass (which I use often)it will show right through and look terrible. So even if you come across something I haven't mentioned to stay away from - make sure it's at least a clear glue/adhesive.
I strongly recommend UHU brand mosaic adhesive. It's a clear adhesive that is very strong but if needed, you can easily remove your glass. It's water based amazingly but it's unexpectedly strong. It also drys at good rate. And it's cheap. Apply it with a paint brush to assure an even coat. You can find this adhesive at craft stores such Micheal's and A.C. Moore. Some stained glass resellers/studios carry it. But I suggest buying it from a store because resellers tend to inflate prices.