If it's anything like previous versions of Windows, you can just pop the disc in the drive, and it will ask you if you want to upgrade.
Alternately, since the computer you bought with Win7 can't be more than a few days old, you could just decide to blow away Win7 Home Premium and load on Win7 Ultimate. How much could you have possibly done to customize it in the space of a couple days that you couldn't redo in very short order?
I just purchased a PC with Win 7 Home Premium pre-installed. In the meantime, I was able to purchase a copy of Win 7 Ultimate through my campus bookstore for a good price! How do I go about upgrading from Home Premium to Ultimate? Both versions are 64-bit.I do have a physical disk with Win 7 Ultimate. So, please do not direct me to Microsoft's Universal Upgrade Program for Win 7.