Futon frames almost invariably consist of four major parts and some hardware to hold it all together. The decks come apart and you can also remove the brackets if you want to protect them from damage in shipment. Pulling a futon bed apart is a lot less awkward than putting one together. Gravity still comes into play though.
Lay the futon frame flat and in its bed position.
Remove the seat deck from the transmission clips. The seat deck and the back deck are affixed to the arms using brackets called transmission clips. Unbolt one side first with a standard or Allen wrench and have a buddy hold the seat deck in exactly the same horizontal position it would be if it was still attached to the transmission clip on that side. This is important because it stops any stresses that can make removing the bolts from the second clip hard.
Remove the seat deck from the second transmission clip and, with your buddy, remove the seat deck from the assemblage.
Follow the same procedure for the back deck. The back deck is the deck that makes up the back of the futon.
Remove the stretcher. The arms aren't joined by the seat or back deck, but by a stretcher--a rod. Lean one frame arm against the wall and have your buddy hold the other arm vertical and the stretcher horizontal. He will need two hands. Remove the bolts holding that arm to the stretcher with a standard or Allen wrench. Have your buddy keep holding the arm and stretcher to reduce stresses.
Unbolt the second arm from the stretcher with a standard or Allen wrench and lower everything to the ground. You now have a disassembled futon frame.