If there's sufficient difference between the lightest part of the subject and the darkest part of the background, you can often just do a Curves operation (or add a Curves adjustment layer).
If you have trouble with the adjustment adversely affecting your image, or some of the background remaining, you can clean things up with the Dodge tool set to Highlights and a low Exposure level.
Lastly, if you want transparent surroundings, the most accurate method (and most likely to work with just about any background) is this: You can select your subject using, say, the Quick Select tool, [Refine Edge], then use a layer mask to just hide the background. Russell Brown describes something very much like this in this video:
Once you get the hang of it, that's a very powerful method. Using Select/Refine Edge in just a few moments...
Transparency makes it possible to put whatever color you like behind her, and even stuff like this is possible...
Thanks and that is good information. I love the Russell Brown show.
The technic works well accept for where the hands and feet meet the white....
Well, to be fair some of those parts aren't actually IN the original photo to begin with - the wrinkles of the fabric are blocking the view.
I suppose now you'll want to learn how to paint parts of hands and feet in...
You are absolutely correct.