...
Ok, let's start off on what
not to do, taking the magic wand:

And trying to render it that way.
You'll never be able to do it. Really.


See all the mistakes the algorithm made?
So, what we need to do is first to use the pen tool to make a selection:
PEN TOOL IT!If you do not know how to use the pen tool, shame on you. Here's a tutorial I made a while back which could help you, there's tons of Pen Tool tutorials on the internet as well:
Pen Tool TutorialYou don't want to pen tool every single detail - that'll take way too long, and doesn't apply to this image, since there are semi-transparent elements. All you have to do is put the solid colors into the selection:
{Pen tool path highlighted in green)

Note that the pen tool path in white spaces between the hairs and the one between her arm and leg are
separate paths. You do those separately from the main outlining path around her, preferably on a different
path layerNow, we're going to convert the pen tool path into a selection.
So, selecting the
main path, make a selection from it by pressing ctrl + click:

Then, press ctrl + alt + click on the pen tool layer you put the inside paths to. This will subtract those selections from your current selection:

This is roughly what you should have by now:

(You may play around with the feather settings now if you wish to. Personally, I like to do that last as the final stage, but that's just me).
Now, we move onto extracting the render.
So, in your toolbox, select the background eraser:

Use these settings:

Now, here's the tricky part.
As the tool's name implies, the background eraser erases the background, or rather - the background you set in your background swatch. Of course, the background swatch for this image is white, as that's the background color - the tricky part is to select a foreground color which allows for the correct amount of foreground to preserve.
If you use a foreground color too light, you will get a lot of background artifacts (white) in your rendering.
If you use a foreground color too dark, you will erase too much detail.
Here's some regions I recommend would be a good place to pick out your color:

After you got your color picked out, it's time to go crazy with the background eraser! Oh yea, It's always nice to use a black background to check your extraction work when your image background is generally bright (and vice versa). This allows to catch mistakes you generally wouldn't catch on a lighter background color.
Just erase away:

And now you're pretty much finished, I messed up this time and picked a color too dark and got this:

Now, you just have to go in with the background eraser (after deselecting everything) and get those white spaces around the hair stands missed during the initial extraction. Make sure not to damage the skin!!
And yea, after some final touching up you should get something like this:

And yea, you're done!