Run the installer that you got from Filemaker Inc. on the new computer and enter you license key just like you did for your primary computer.
I cannot find the installer on my computer. Is that a file I can download from the FMP site?
It's what was used to put Filemaker on your original computer. If you cannot find it (was it on a CD or DVD from FileMaker or did you get a downloaded installer?), you'll need to contact FileMaker Customer support with proof of purchase to get a new copy of the installer.
An email from Filemaker may contain infomation.
The default location for Downloads is OSXHD > Users > youruser > Downloads folder