Get a tool box and crawl under the truck and start removing every nut and bolt that looks like it is attached to the bed, when you get them all it will come off.
Actually, you are into it a little worse than just removing bolts. Save all the hardware for reassembly! You may want to tap out all the (doubtless rusty) holes, and run all the bolts through appropriate sized dies, to make sure that you can get the beastly tjing back together and still look professional.
1. Unscrew the gas tank filler. You will see 4, #3 phillips screws facing you. Remove them and dismantle the filler neck, which has a square plate that holds a rubber flange around the filler tube. Push the filler tube inside the bed and make sure that the cap stays on the tube.
2. Inside the bed, you will find either six or eight Torx(tm) bolts. These are invariably rusted solid. Before you attempt to remove them, go from above and below with a propane torch, heating the bolts enough to break the rust in the threads. Do not heat them enough to blister the paint. Next, soak them overnight in Liquid Wrench (not WD-40, as WD-40 will burn) and wait until they loosen that pivotal little amount.
3. You will find either one or two electrical plugs that power the lights, trailer controls, etc. Unplug and mark each connector so you know what goes where for reassembly. Many times, on older pickups, you will find "modifications" for camper tie-downs and trailer equalizers. These should be on the frame but I have seen many instances where people have mounted them to the bed metal. Once the bed is off, correct that mess.
4. After the penetrating oil has done its job, slowly and patiently move the Torx(tm) bolts back and forth until you can remove them without snapping. Easier said than done but your patience will be rewarded. Do not be too surprised that you must use a cheater to develop the power you'll need to move the bolts.
5. Check all the mechanical goodies, paying particular attention to real wheel bearings, seals, differential, hydraulic lines, electrical lines, rear end, and if you value your truck enough, give it a good (usually overdue) cleaning. The lights come out in units, but make sure to clean out the plugs before you hook them back up on re-assembly.
6. Do what you intended to do (usually a paint job) and reassemble in reverse order.
It is about a day's job and takes two strong men to lift the bed off, and the same two clever guys to lift it back on.
Well I agree with Elden on getting under the truck and start removing bolts, but that also has to be done in a proper way. This is to ensure that you do not accidentally open any other component, I have been using these online set of instructions http://www.automotix.net/autorepair/diy/ford-f_150_pickup-repair.html which will guide you in the process of flatbed removal. I myself have been using DIY from here and they are laid out in a very easy pattern which everyone can understand.
Other people asked questions on various topics, and are still waiting for answer. Would be great if you can take a sec and answer them