First thing, you need to select a picture. I will present this on this picture that you can see. I will sho how to do this by using GIMP. (There shouldn't be much problems with other programs.) For this method we need free select tool aka Lasso.
Tutorial Image 1
Now, select any point you want to start selecting your character. It's not that hard, simply place nodes along with your character outline. The closer placing of notes, the more precise your cut will be.
Tutorial Image 2
Now, continue until you select outline of your character completely. Ignore for now any background hair.
Tutorial Image 3
If you have finished your main selection, now we can take care of any background that was selected together with our character. Continue using yor lasso tool, but change its mode to "Subtract from current selection" aka removing selection. And now do the same way as at beginning at deselect any background that was between hair, legs etc.
Tutorial Image 4
Only one thing left to do, cut our character out of the picture and paste it to new one or invert your selection (CTRL + I) and delete background.
Tutorial Image 5
It's finished. It does not look that great especially ends of hair, but this is only because I wasn't that precise while making this.
It can take a little time, but final effect is really good.