Try to draw from top-right to bottom-left - or the other way round if you're left-handed - and place a sheet of paper under your drawing hand. Copy paper is smooth, and so smudges easily, which can be remedied either by using a harder pencil (less prone to smudging) or using drawing paper. Depending on what weight and make you get it doesn't have to be expensive.
Copy paper is very smooth and has no texture or 'tooth' to hold the graphite on the sheet. That's why any little touch smudges it so bad. You can certainly get around this by using the techniques others are discussing, but the problem would also be minimized if you got some drawing paper, even relatively cheap drawing paper. It'll still smudge, just not to the same degree. Also make sure you have a good eraser, I like the white Mars Plastic ones.
A lot people do that- you can fiddle with the Brightness/Contrast levels, Curves, then use a large brush and sample the background colour ( since traditional paper is never pure white) and clean up the remainder.
I would recommend starting your drawing by using a harder 2H pencil which doesn't smear as much. Its likely that most of your smudging will happen in the early stages of the drawing as you move from broader strokes to more narrow and focused ones as you refine your drawing. You can start with the 2h to get the refined features of your image on the page and then switch to the softer HB and B pencils when you've moved on to the shading stage.
However, placing a blank piece of paper under your hand and wrist is also a really good tip.