I presume Adobe Premier Elements license is the same as for Photoshop and Lightroom.
As a first step create an ID at Adobe, assuming you have not already done so. Then register your software.
I'm rather surprised that you say you are only allowed one copy, as normally you are allowed two installations. Back-up your download, I normally keep two one on HD and second on DVD, then if you wish to move your copy from one PC to another Deactivate your first installation by going to FILE DEACTIVATE then you will be able to use Elements on a different PC.
The full license can be viewed at License