>>2191725I use GIMP, but this should translate fairly well to other programs.
A good starting place for something with a solid bg like this one, is to do a fuzzy select of the bg. If your threshold is too tight you'll have a gap between the bg and the character, if the threshold is too loose, you end up getting parts that you don't want to mask out. Play with it til you're close enough.
Expand your selection 1-3 pixels. The more details there are, the less you'll want to do this (as it will cut off tips of sharp objects, or completely claim thin pieces of hair: see eye lashes in attached picture).
Feather your selection 1-3 pixels. This is dependent on a few things, but mostly how thick the linework of the drawing is, and how close you were able to get. Again, play around, ctrl+z is your friend till you get a good one.
Then, mask out the selection to be invisible (or invert selection and mask selection to be visible; same song different verse).
At this point, l would have another layer that isn't masked, and cycle it on/off a few times, see if there's any obvious things that got masked away that shouldn't be. Bring them back by drawing on the mask itself (white makes it visible, black "erases" it).
Then, as a final check, make a layer with a solid color that isn't prevalent in the linework (I generally use a brick-red) and put it behind your work. This will let you see minor imperfections that can be corrected.
Attached is an image that just goes to the masking step. I didn't do any detail work on it. You can see that I didn't go back in and touch up the eyelashes, the tips of the hair are a little weak (but passable), and there's a spot near her collar that still needs to be masked out, but the rest of it looks pretty solid.
Hope this was helpful.