Very very hard to get the bits around the person to look right.. It either looks too harsh, with sharp edges and a lack of detail or the original not quite white background is visible.
The 'right' way to do it is with a paper background, a couple of lights, one for the subject and another to overexpose the background.. Setup the first light so the subject appear nice in the pictures, then setup the second light to only illuminate the background, and to be 1-2 stops brighter than the subjects illumination.
do a search on seamless paper. you'll need a stand for the roll too.
vuk.
p.s. you can also take your model outside and look for a wall of the right color.
You can shoot a portrait with a black background against white paper.... By simply ensuring your flash/light illuminates the subject and NOT the background.. The background will come out underexposed, and if ambient light is low enough then the background will be black.
What equipment do you have? The pop up flash is not really suitable for this task as its a very direct light source..
For a background you can get your hands on a lump of suitable cloth/paper for not a lot, and with suitable clips can attach it to a curtain rail (I use the rail above the doors into my conservatory)..
If you cannot afford an off camera flash (either studio or portable) then head outside around an hour or so before sunset, find a suitable backdrop (walls covered in plants are good), get your subject to stand 6 feet or so away from it, use a narrow(ish) DOF to seperate them from the background by making the background appear blurred and use the on camera flash or a reflector (large bit of card covered in silver foil works well) for a spot of fill light and have a play. Cheap and very effective.
Have a read of the strobist (
http://strobist.blogspot.com/) if you want to start learning to use off camera flash... VERY good site!
Sam