I find that baby wipes work pretty well to get most of the makeup off. (you'll still need to wash your face to get all of it off though). Another tried and true method is cold cream (the stuff by "Ponds"), it takes off most makeup. The only thing that requires special treatment is waterproof mascara (which is a real bugger to get off). For that I use a dedicated eye makeup remover (you need to make sure you get one that says "Removes waterproof mascara" somewhere on it (I use one by Neutrogena). I put it on those little cotton round disk things and hold it against my eyelashes for a couple seconds before rubbing the mascara off. The trick is, that you normally apply mascara to the bottom side of your lashes, so that is where you need to remove it, so you'll need to drag the cleaning pad upwards to wipe off the bottom of your lashes. Also be aware that dark lipstick can, and will, stain your lips. A lot of lipsticks are specially formulated to stay on your lips, so it's pretty difficult to get all of it off.
As a closing note, I will remind you of the number one rule of makeup for ladies. Use makeup to highlight your eyes OR your lips, but never both. If you opt for bold lips, use understated eye makeup, and if you opt for bold eye makeup, used understated makeup on your lips.
J.