For pieces which are soldered together, you would need to repair stained glass using welding flux, soldering tools and supplies and metal the same as the material used in the piece you are repairing. Consider also the thickness of the metal solder from the original design and match as closely or exactly as possible. Initially, you may place back the piece using glue, once it has finished curing. Apply the welding flux to ensure that the metal solder adheres to the surface and material and use the soldering iron to complete the process. Wipe off any residue with a damp cloth and use soap or cleaning agents commonly used or recommended to remove welding flux and other glass residues.
In certain cases, you may need to detach the entire set from the base or holding area to repair stained glass. Be sure to have someone to assist you when working on larger pieces or areas to avoid further damage or accidents. In cases of cracked or broken glass pieces, you may need to source out the same material and color of the missing or broken pieces and cut newer pieces. Be sure to use proper working tools such as gloves specifically for working with glass. For these types of repairs, you may need additional tools like a glass cutter and sandpaper to smooth out the edges of glass pieces to be reinstalled. You may use regular tracing paper and a pencil or market to make patterns of the damaged pieces placing the paper on top of the piece, tracing along the missing areas.
There are available protective coatings for glass in wax or liquid form to protect stained glass pieces from any stains, light scratches and to even out and even restore colored glass. You may find these in your local hardware store.