The process is easy. You have to install All My Books on your new computer.
The latest All My Books version is available for download here:https://www.bolidesoft.com/software/amb_setup.exe
Then activate the program with your activation code. You can use our automatic registration details reminder here:https://www.bolidesoft.com/a/user/
To transfer the database, start All My Books on your old computer and use the menu item "Database - Backup..." to save the database file to some removable media, like a USB flash drive. Then copy the database file to some folder inside the Documents folder on your new computer and open it with a double click.
Please let me know if you need any further assistance.