A dialysis machine takes your blood out and runs it through a specialized osmosis filter and then pumps it back in. It works based on osmosis (flow of high concentration to low concentration) The blood flows on one side of a semi-permeable membrane whose pores are too small for large proteins (1um or so probably) so blood cells, hemoglobin etc is left alone. On the other side is special fluid that pulls the urea and other waste fluids from the blood.