Downloading is the the process of copying a file from an Internet site to your computer... when you downloaded, what is the location you told the download manager to use for the saved file?
Installing is when you click the program download and it TELLS you that it is installing... which will include putting a program icon on the desktop and/or in your list of programs
So... which did you do?
Also, since you are new the program, some reading
Online User Guide http://help.adobe.com/en_US/premiereelements/using/index.html
-Page to download current PDF http://helpx.adobe.com/premiere-elements.html
Importing Video http://forums.adobe.com/thread/1065281
-and project settings http://forums.adobe.com/thread/1112086
Saving & Sharing http://forums.adobe.com/thread/1137128
-Sharing to DVD or BluRay http://forums.adobe.com/thread/1137645
-Sharing for Movies http://forums.adobe.com/thread/1051093
-Sharing for Computer http://forums.adobe.com/thread/1058237
Steve's Basic Training Tutorials... steps are the same for several versions