The outer frame is wood, but the window part is 'leadlighted' or appears to be, the material's gold/sort of brass. At first I thought it might be one of those fake overlay things over a solid piece of glass, but if you gently push on the window, it seems to give a little like you'd expect a leadlight with individual panes to do.

So, in order to reglaze, I'm assuming the process would be to remove the beading, supporting the glass from underneath. Lift the frame off, exposing the whole glass part. The pane is in one of the corners (so I assume the way it cracked, it might have been too tight of a fit) so I was figuring the glass section will just pull out if there's no leadlighting around the outside, or cut it away, ease up the other edges, remove glass, insert new piece, etc.

Does this sound right? If it is indeed a solid piece of glass, this metal must be glued on, there's certainly no gap underneath.

For an edge piece you can cut the came (jewelers saw), remove the broken glass piece, clean out the groove in the came carefully, replace the glass, solder over the cuts, then re-putty the glass into the came.

Look under 'stained glass' for the general methods and techniques.