A leaded glass window such as stained glass isn't difficult to repair. Since a lot of detail is usually involved with leaded glass, it will take a lot of patience, and some experience in glass cutting and using a soldering gun is very helpful.
Step 1: Remove Window
Removing the window from the frame is the best method to fix a leaded glass piece. This will allow you to lay the window flat and work up against it very closely. One the window has been removed, trace around the frame on to a piece of cardboard or plywood. This will give you a pattern to work with when you start repairing the glass.
Step 2: Remove Broken Pieces
Start preparing to remove the broken pieces of glass. You will need to heat the solder around the broken glass to separate it from the lead. After you have loosened the solder and lead from the glass, you will want to place clear tape over the broken pieces. This will serve two purposes. One, it will create a pattern to use for the new glass, and two, it will make it much easier to remove the broken pieces.
Step 3: Set Up the Template
Nail down the template panel you created earlier. This will keep the template in place, and will allow you to have a pattern for the window you are working on. This is important as it helps you keep everything in place, and have an accurate representation of the actual window. With this in place, you can have the glass cut that you need for the fix. Use the taped piece you pulled out as a template for the new piece.
Step 4: Apply Lead Came
Slide the replacement glass in to the lead came. Use a glass hammer to gently tap the glass in place. Nail the outside lead in to place, ensuring the glass in secure. Cut a piece of zinc to match the panel and nail it in place. Be sure that everything still fits inside the pattern you created.
Step 5: Soldering
Now use the solder gun to start soldering the joints on the bottom part of the panel. To avoid melting the came, use just enough heat to solder these pieces. Continue to work with the solder gun until all the solder lines are complete. The new lines will likely be shinier than the rest of the window. You can solve this by using an ammonia based cleaning product on the cooled solder. This will darken the lines and help reduce the shine.
Step 6: Replace the Glass
With the piece fixed, you can start to add it back to the original frame. Gently place the glass back in the frame, and use a silicone based caulk around the frame. This will help secure the new piece of glass in place. Tap the frame gently with the hammer to create a tight bond. Install the window.
If you are uncomfortable trying this project on your own, you can always have a professional do it for you. There are many glass studios that specialize in these tricky repairs.