1) Open your image on Photoshop, selecting RPG color scale. For this time I'll be using a Johnny Depp photography.
2) We'll use the quick selection tool. When you have selected it, you'll see the options on the top of the document, you can select to add a selection (+) or rest a selection (-).
3) With the adding selection, start to select the background around Johnny, if it passes over him, then use the rest selection to get that part off. When you arrive to the hair, let some background around and try to don't select the hair at all, like this:
4) When you have all the background selected, cut it, and you'll have your character with a white background. Then go to Select/Inverse. Now you will have selected the character instead of the background.
5) You don't want to loose that selection! Go to Paths and click on the circle marked with red, that will make a Path Layer with the selection, so now just click on the green circle to get the selection again. This will help you to don't have to start it over
6) Now, we just have to refine the edge of the selection, to get that extra background out of our hair, go to:
7) You'll have a little window pop out, you can play with it to make the tool as you want, but as default will work all right. What you need to do is to pass the circle around the areas that have background, like the hair.. you'll see how starts to get whiter and softer (you can comparate the right to the left side)
8) Now, you just have to cut the selection going to Select/Invert. Feel free to do this steps until you get the desirable border. It's better if you go for pieces and leave the hair for the last part.