First, let’s ensure your data is backed up.  All data is stored in a file named database.data.  Copy this file to another location for safe keeping:

http://support.discgear.com/forums/29883/entries/37286

You will also need to get this data file on your new computer, so sending it to a thumb drive, or being able to send it over your local network is helpful.

Next, download and install the latest version (v1.61) of Discware Lite - Non Java VM version recommended for Windows users:

http://www.discgear.com/support/discwarelite/update/

Once updated, use the File, Import feature to import your data from the old computer.   Locate this file on your old computer, copy it to your new computer – somewhere easy to find link your desktop – and import.