More specifically, the first time you run the launcher, it'll ask you for an install directory. Set it up to anything other than your desktop.
If you want to move stuff now, you can change the settings in the launcher, but be aware that you should copy over your saves and whatnot beforehand - actually, to be safe, you should copy over the entire directory. I've done that before, it works fine. If you don't copy it over, the launcher will just start up a new minecraft installation in the new directory.