How to Fix a Broken Pipe Inside a Wall
Fortunately, I have access to the other side of the wall through the garage, so I cut a hole and installed a valve upstream of the break. I didn't have time to do a full repair and re-route the pipe outside, so that's where I've left it for now.
It took three separate trips to Home Depot -- represented above by *'s -- which seems about average for me and plumbing disasters. Things I could have learned: try to remove the broken item before going to get parts. That would have saved one trip to get the additional length of pipe.
I don't think I've ever soldered copper pipes in a non-emergency setting. Last time, our hot water heater failed the day before my parents arrived for a week's stay. If you'd like to do your own plumbing, I strongly recommend learning to solder on a project that doesn't require the water to the entire house to be off.
Thanks to zachninme for taking photos!
2008-08-31 Update: Since I know everyone is dying to know how this turned out, I've add a few more pictures. With the right tools and parts in hand, I replaced everything from the broken copper pipe out to the hose bid, and removed the valve inside the wall. The tricky part was mounting a brass 1/2 NPT female to copper 1/2 elbow. Originally, this piece was nailed into a stud and then the copper was soldered on before the walls were finished. I didn't want to make a big hole in the stucco on the exterior wall and I couldn't safely get my torch into the confined space, so I soldered some copper elbows onto this brass elbow and then mounted it with machine screws coming in from behind through the stud (screw heads on the inside where I could access them through the hole in the drywall, and bolts on the other side with the brass elbow where I positioned and tightened them by feel).
Having opened a plumbing battle on this front, I decided to fix a bunch of other plumbing problems around the house, which I'll write about shortly in an Instructable.