How does the exhaust pipe connect to the muffler?

Answer: Welded on

Below would be how to repair if the muffler has broken away from the exhaust pipe.

If you have a welding machine:

If your just attaching the muffler, You would need to attach the muffler to its hanger, then find a way to secure it to the exhaust so you can then weld it in place.

If you do not have a welding machine:

Most auto repair shops, have a welding machine so that they can do these kind of repairs if you lose your muffler, you can also purchase some special muffler/exhaust tape to tape around the break. Using the tape is a temporary fix.