I am assuming that your new computer has Windows XP or Vista? If yes, you need to consider upgrading your Generations v6 to the latest Generations version 8.5a. You will gain compatibility with Windows XP (works on Vista too), bug fixes, and enhanced facilities such as the ability to display photographs on the family cards.
To transfer your data the easiest method is probably to e-mail your .uds family file to yourself. Or use a USB memory stick if that is possible on your old computer.
Install Generations v8.5a, then copy your .uds family file to the new Program Files/Generations folder.