I've had to do this twice now.
Theres 2 ways. If you are using a Windows based system you should be able to use the Microsoft Easy Transfer and it will "ghost" everything over to the new system through usb to usb connection
the other way would be to manually export anything custom you have, recipes,inventories, equipment.
That just involves highlighting it, naming it and putting it on a hard drive to reimport once you install beersmtih on the new computer.
The first method is the most painless and should bring everything you need over including beersmith