How do you fix a copper pipe that burst?

There are many ways to fix a burst pipe, if you are experienced in soldering you could re round the pipe closing the burst portion and solder the cracked section, or simply cut the burst section out and solder in a new piece withe two couplings. For the less experienced I would recommend cutting the pipe and using a shark bite repair fitting, it comes with detailed instructions and is made just for the situation you described