Soak the cotton wool pad with some waterproof eye makeup remover (I've found Boots No7 to be quite good).
Hold the cotton wool to one eye, press gently, and hold for a little while to 'soften' the mascara.
Gently wipe downwards with the cotton wool and most of it should come off in one go.
If not, a couple more gentle downward strokes to remove the rest (don't rub in circles, you'll end up with bald eye lids!).
Repeat with other eye.
Splash with water to remove the slightly oily feel the remover will leave.
Finish off with a gentle eye cream.
Agree with My Angel Pie, Johnsons wipes work well too, same process but you won't have to saok them first!