Just instalkl it like you originally did using installation files. You are allowed to have two activated installations so you do not have to remove it from thePC if you would like a backup installation.
If you you need to download it and originally purchased it from Adobe then there should be a download available thru youyr Adone account online. Otherwise, you can download the trial and use your serial number to activate it to full use.
PSE 12 Trial - http://www.adobe.com/cfusion/tdrc/index.cfm?product=photoshop_elements