Recently my wife smashed my laptop off the floor damaging the screen and it will not power on, so I bought a new one. My question is how do I recover music off the broke laptop to put onto my new laptop. Any ideas

Don't know the best way, but one way is get a 2.5" enclosure. About $10.00.
Remove hard drive out of old computer install in case. It has a USB connection, then plug into new laptop.

Can't I just run usb to usb and do it that way or will it not work

USB doesn't work that way. The best solution is what Stratmando suggested. Removing the drive from most laptops is pretty straight forward and you might have a mounting bracket to remove as well. Connect the cable in the enclosure to the drive and close up the enclosure. Depending on the drive you may also have to connect power to the drive as well. Plug it in and assuming the drive wasn't damaged in the fall you should have no problem accessing the files on the drive. If the computer won't power on there's a good chance the drive was damaged as well.