When using a white background it is very important that it is not overlit. The white background will act as a reflector and bounce a huge amount of light back towards your camera and onto the back of your subject.
Many magazine articles and a few enthusiastic camera club members have told me that, to get a pure white background it should be over-exposed by two f-stops! I can tell you here and now that this is nonsense!
A white background, if correctly exposed will reproduce as white - because it IS white. If you overexpose it by 2 fstops it will throw back so much light it would overexpose the edge of your subject so much, that you would lose all the edge definition (especially around the hair). You can
see the effect here - notice also that because of the flare in the lens the whole image has become de-saturated!
The easiest white background is obtained by using smooth uncreased paper or a white smooth wall. White paper only requires between 0.5 and 1.0 of an f-stop more than the subject to ensure a clean, pure white background.
White cloth backgrounds require a little more light to burn out the creases but this has to be very controlled . I would recommend that you have no more than 1 f-stop more on the background than the subject.
Tip: If shooting digitally, turn off the front light(s) and take a picture. Check your preview screen and your subject should then be a silhouette. Any loss of edge definition will be easy to spot!