Remove sheets and pillows from the futon. Locate and untie the futon mattress strings that may be holding the mattress to the futon frame. They may be on the back, underside, and edges of the futon.
Lay large towels outside on a sunny and warm day in an area with good air circulation.
Place the futon mattress on the large towels and allow it to sit outside in the sun for a few hours. Flip the futon mattress over and allow the other side to dry out for a few hours.
Bring the mattress back inside after each side has been exposed to the sun for a few hours. Put the futon frame into the bed position and place the mattress on top. Do not yet reconnect the string ties.
Plug in one or two fans and face them at the futon. If you have more than one fan place one so it blows under the futon and another so it blows air over the top. Flip the futon mattress after an hour or two and continue to blow air around it.
Use the vacuum cleaner with hose attachments to clean both sides of the mattress. Re-tie the tie strings to secure the mattress on the frame.