There are a lot of so called "glass glues" on the market. My personal favorite is 100% pure silicone. It is available in small tubes for odd jobs or caulk tubes for everything else.
Make sure you have ALL the pieces before starting. dry fit the parts to make sure you know which goes where. Apply a small bead of silicone to the surfaces to "glue" together. Sometimes a piece of masking tape helps to hold everything in place while the silicone cures (24 hours, you can handle it in an hour or so, CAREFULLY) Don't worry about putting too much on, once it cures the excess can be trimmed with a razor blade.
Also silicone is available in many colors and clear. Silicone is what holds fish tanks together. that's ALL they use.
Silicone stinks like vinegar so you might want to do it in the basement or garage. it cleans up with paint thinner. I would wera rubber gloves.