Ideally, you should create your backup using your LNS-based network management tool. For example, LonMaker and Izot CT have Backup and Restore features which make it easy to create and restore backups.
If you don't have these features available, you can manually find the database files and copy them onto your backup drive or computer. The database files can be located anywhere but are typically located in C:\lm\db\YourProjectName or C:\Users\Public\Documents\LonWorks\OPenLNSCT\Databases\YourProjectName
The database folder will contain at least 4 sub-directories called "db", "Eventlog", "recovery" and "VNIs" and some files such as objects.idx and objects.dat. The entire content of the folder needs to be copied over to the new computer.
If you then need to import the copied project into the LNS global database onto the new computer, you can follow these instructions HOWTO: use the LNS Object Browser to add a network into LNS (KB1020)