I have a sofabed whose back is fixed to the bed by bolt and nut. When I try to loosen the nut by wrench, the bolt and nut move together. There are no rust. How shall I loosen the nut?
Update: the head of bolt has a shallow hex hole. I have got help from another who used hex wrench to stick into the hole of the bolt head and fix/rotate the bolt, together with a regular wrench to rotate the nut.
Best way: put a wrench on the nut and the proper driver or socket into or over the head of the bolt, and turn one while keeping the other stationary.
Second best way: put a wrench on the nut, and a pair of locking pliers on the shank (threads) of the bolt. You WILL damage the threads of the bolt; just try not to cause so much damage the nut won't come off. This is the only way besides cutting to remove a carriage bolt, which has a flat or a smooth dome head that can't be "locked on" with a socket or driver, or to otherwise remove a nut from a bolt when you can't get to the head.
Seriously though, you'll have to find the head of the bolt and hold that while you turn the nut (if you're not already doing that, which it sounds like you're not).
If you hold the bolt but are still unable to turn the nut, you may indeed need a little penetrating oil. Spray a liberal amount of the oil on the nut and bolt, wait 5-10 minutes (longer if the bolt is really rusty, which it doesn't sound like it is in your case) then try to loosen the nut again. You'll want to put a towel or rag under the bolt to catch any excess oil that may drip off.
You need to get something on the head of the bolt to stop it from spinning. The tool depends on what the bolt head looks like and how much space you have available.
Low tech solution with just some spanners, wrenches
My use case was removing seats from a bus. These were bolted in through the floor into nuts below; whole nut-bolt assembly rotated together. Nuts and thread below naturally quite rusted.
My bolt heads were hex, that were NOT flush into the cabin floor. This meant I could lay a spanner flat on the floor, holding the bolt head.
Now, if you have a spanner or adjustable wrench or locking pliers long enough that its handle can strike some immovable fixture above when turned clockwise in the cabin i.e. at the bolt head, then turning the nut counter-clockwise below will turn the spanner clockwise above, so that it strikes and pushes against that surface, which could be e.g.
I'd lay my spanner flat on the floor with ring end over the bolt head, and placing its handle just left of (counter-clockwise of) a surface that would stop its rotating clockwise, then drop a heavy object that won't slide off, e.g. a sandbag, on top to keep the jaws of the spanner from popping off the bolt-head. Then I could unscrew the nut counter-clockwise, below the vehicle.
Assuming it is a carriage bolt with a smooth dome shaped head and without a square shank on the underside.
Method 1: Squeeze some superglue around the head of the bolt. Wait a while, then try unscrewing the nut again.
Method 2: Drill a small hole, say 1/8 inch diameter at the edge of the dome head, at an angle, say 45 deg.to the bolt shank, about 1/4 inch deep, insert the drill into the hole to lock the head from rotating when the nut is being unscrewed.
The hack saw thing didn’t work. Locking pliers did. This was the slot I cut, but I just couldn’t find a screw driver that would hold it firmly enough. I also tried drilling - no luck. And regular pliers. That’s what probably really damaged the end of the bolt as the bolt would just spin in them. 
You could get a hacksaw and cut a notch in the end of the bolt, then use a screwdriver to hold it.
My advice. Get a crowbar and stick it under screw. With one hand you push lewer and the other hand spin bolt. The rule is nut from other side will be pressed and will not being able to rotate. With aku driller goes easier and faster. Time plays role. You are getting tired of doing a lewer. So. I do look how to reverse process. I need to mount a nut on a screw from other side without making an counter with wrench
