If it is a flat image, duplicate the background layer and then delete the original background layer. You can then delete selections of the duplicated to make it transparent.
If the edges are well defined around the subject in the photo, make sure that the Magic Wand's "Contiguous" box is checked and adjust the tolerance. That is the amount of levels it selects that are different from the source point, so that it selects most of what you want.
If it makes a good solid selection you might want to click Refine Edge… and feather it a bit. You may want to try the Quick Selection tool as well.
After you get it selected you can just hit Delete and it will remove the selected stuff. You can then go back over it with the "History Brush" and paint back in the parts you want to keep but removed.