The desktop PC you want to connect to must first be one of the following, AFAIK:
Windows XP Pro
Windows Vista Business, Enterprise, or Ultimate
Windows 7 Pro, Enterprise, or Ultimate
Windows 8 Pro, or Enterprise
After that step and after setting things up, you're technically logging into the desktop and using the applications from that platform, viewing on your Surface (you're not actually running any other software on your Surface besides the Remote Desktop client/app itself). Yes, you can download and install stuff onto that desktop PC while you're logged in remotely from the Surface; it's just "remote control" really. There are tutorials online; I've never done it myself except a few times at work via work machines, because my home computer is Win7Home and my workplace doesn't allow non-company machines to connect.