Lay your memory foam mattress over a platform bed frame or any other solid, flat wood bed surface. A box spring usually has sagging spots that will encourage the mattress to roll up or develop lumps.
Cut a piece of plywood sheeting to match the width and length of a box spring and put the sheeting between the box spring and the mattress. If you do not want to replace the box spring with a new frame, the plywood will provide a flat surface. As you sleep on the mattress, the pressure of your body against the plywood will flatten out lumps.
Lay a fitted sheet over the memory foam mattress. As you put the fitted sheet on the mattress, tuck any curled edges down so the tension from the sheet holds them in their proper position.
Sleep on the mattress nightly. The pressure and heat from your body will flatten out the mattress through frequent use.