As there is two techniques for building stained glass, (using lead canes or copper foil) thus there is also two standard ways to repair any given panel.

Leadlight repairs

Significant damage to glass and lead canes not only looks distressing, but will also lessen it's strength and possibly allow the rain and wind to get through a window. Repairing damage makes a lot of sense but can be a difficult process. If you are very lucky, the broken glass / distorted canes are at the edge of the panel and are relatively easy to access and repair.
Most cases however are not so easy because the breaks are deep within the window's design so the window has to be literally cut in half to get to the repair area. Even worse is when the grout in the window is in great condition, and it's holding on to everything really well. Strong grout can be a real headache because it hinders a clean separation of the parts.... :-(
I have encountered these problems and have developed a technique that solves all of them, so you are very lucky today because you are about to learn a superior repair technique... :-)

The first job is to remove the panel from it's vertical framed position. If at all possible, remove it frame and all. i.e. a hinged panel is so easy by unscrewing it at the hinges. If the panel has wooden beading, consider yourself lucky as the beads are still easy to remove. This task becomes difficult only when it is installed with window putty.... DOH. If so, you'll have to be careful and patiently chisel out the offensive putty. Take your time with this.... and good luck!

Now that you have the damaged panel at your workshop, handle it with great care especially when lying it down flat on the bench or when turning the panel over. If the panel is still within it's frame, consider yourself lucky as the frame provides edge support. Framed panels must however have support from below when lying flat, so fold up a cloth towel to just over the thickness of the frame depth and position this under the horizontal panel. The folded towel takes all of the weight.

Apart from the usual tools of our craft, there is one tool needed to effect any repair. This is the right angled pliers. It is used to break out the broken glass.

Because of their right angled handle, it can break into and remove glass like no other tool can.
Get one of these....!

Important tips for repairs

The following Youtube tutorial video demonstrates repairing a curved leadlight panel in detail. My technique can be applied to any leadlight panel providing it is repaired horizontally on a work bench.

Youtube Video
Repairing a leadlight panel

Copper foil repairs

Fixing copper foil objects is essentially the same and is a straight forward task.
There is just a couple of minor differences...
* instead of slicing the lead cane open, you melt the solder and remove the copper foil surrounding the repairs.
* Fresh copper foil is carefully applied around the new glass pieces before each is inserted into your panel.