Let's assume physical access to the cockpit is not an obstacle (flight attendant or someone has duplicate key or access code; a crowbar can be obtained; or otherwise a brute force way to get in can be devised.)
I'm going to say the answer to the question is as follows:
If a passenger has never flown a plane or played with a flight simulator, then there's a very slim chance they will successfully land the plane. There has to be some kind of working knowledge of how aircraft work. This knowledge is crucial and simply can't be imparted by someone trying to talk them through it over the radio. (Can a non-technical passenger even figure out how to use the radio and establish communication with a control tower? Probably not. )
However, if a passenger has played with flight simulators, the probability of success rises greatly. In other words, now it's actually in the "tens of percent" (10%, 20%, 30%) versus hundredths of percentile (0.001%). That's because flight simulators are pretty accurate representations of real flying, and in order to use a flight simulator successfully, you actually have to first learn the fundamentals of how airplanes work (gliding, stalling, dealing with wind, how to line up for the runway, etc).
And if a passenger has piloted some sort of real aircraft, then it increases the chances a bit more, although probably not a huge amount compared to the simulator-only case. At this point, it is a matter of the passenger learning where the minimum essential controls are, how to take the plane off autopilot if that's what's needed. Knowing which are the essential controls and ignoring the rest of the control panel. And knowing how to navigate to the nearest airstrip. Assuming this information can be imparted by someone (control tower people over the radio), then I would say there's a 95% chance of making it to the airstrip and maybe a 50% chance of successful landing. As someone else mentioned, the touchdown is the crucial moment. Someone who has landed a single engine prop isn't going to know how a 737 feels.