Hi,
1. Make a full backup of your Documents/BeerSmith2 folder (PC and Mac - Linux is a bit different) to a flash drive (or something)
2. On the new computer, install BeerSmith2 and use the same key you used on your old computer
3. Copy your old Documents/BeerSmith2 folder entirely (from your backup copy) to your new computer's Documents/BeerSmith2 folder
4. Run BeerSmith2 - it should pick up your data
5. When you are all done, uninstall BeerSmith2 from your old computer
Cheers,
Brad