1. On old machine
Open ManicTime, then click Tools -> Backup and restore -> Backup now to backup the database. Keep the generated file, you will need it on the new machine to restore the data.
If ManicTime is no longer running on the old machine, you need to copy this file for the new machine:
2. On new machine
Install ManicTime on new machine. Start the app and click Tools -> Backup and restore -> Restore and choose the backup file from the old machine.