Once the software is installed on the new computer, before running it the first time, you should copy over the other needed files with your data and settings. Settings files are stored in C:\ProgramData\LeaseAccelerator\EZLease. Copy all files from that folder to the same folder on the new computer. This will include the registration information, so you won't need to re-enter that. Note that ProgramData is a hidden folder (and is not the same as Program Files). If you don't see it listed under C: in My Computer (also called Windows Explorer), go to the View menu item and check the box that reads, "Hidden items."
Your database(s) could be in any location you've chosen (the full path is always displayed at the bottom of EZLease when the database is open); if they're on your own computer, then transfer those to the new computer. If you have multiple users, you may have stored the system options file (Options.xml), the account number groups file (Account numbers.mdb), and the lease database in a shared location. You can check the locations of each in System Options on your computer: Text tab, Options store location, and Account numbering, Group database location, shows where Options.xml and Account Numbers.mdb, respectively, are stored. If they're not in C:\ProgramData\LeaseAccelerator\EZLease, you'll need to either move them to a new, accessible location, or simply change the folder setting in the new installation of EZLease.
If all your EZLease files are stored in a shared location, and you copy the EZLease.config file from C:\ProgramData\LeaseAccelerator\EZLease on your old computer to the same location on the new computer, no further setup will be necessary; the config file points to the locations for the other files and contains your registration information, so everything will run as it did on the old computer.