if you cut out something like a person and want to put it on a different background, you're kinda gonna have to experiment til you get a technique that works for you.
here's one way...
duplicate the person. then you should have 2 layers of the same person. take the bottom person and do a gaussian blur with it at like 1 or 2.
then take the top layer and select it. then do a reverse selection so everything but the top person is selected. feather this selection at like 1 or 2. then hit the backspace to delete whats in your selection. that will soften the edges on your top person.
with the combination of both of these it will "hopefully" soften the edges and blend it more to the background.