This Photoshop tutorial by Colin Smith will show you how to change the background in a photo. But it goes way beyond that.
Here is a tip that will show you how to make the old refine edge work in the latest version of Photoshop with a secret shortcut. You will also learn a couple of tips to get cleaner edges on your cutouts, so that they blend in perfectly with the background.
And when you get so pro (or hopeless) that Photoshop is simply too time-consuming, there’s always the Topaz Remask Plugin. It’s not free, but who cares if Nat Geo is calling and you can extract the bear’s fur from the bush in five minutes?