I would say talk some to the pilot before departure. If the pilot tells you anything that contradicts any of this, forget this and go with what the pilot tells you! They know the airplane far better than any stranger you'll find on the Internet.
Ask them to point out the important controls; throttle, yoke or stick, elevator trim, and how to change the frequency on the radio and transmit, will probably get you pretty far. The transponder IDENT button and flaps selector may also be useful, but especially flaps will require a bit of care. Elevator trim generally isn't critical, but it is very nice to have.
Ask them to point out the important instruments; airspeed indicator, altimeter, vertical speed indicator, compass, and fuel gauges, will again probably get you pretty far. Those will tell you where you are relative to the ground or to sea level (altimeter), where you're going (compass), how fast you're going (airspeed, vertical speed), and how much longer you can go (fuel gauges).
The exact control layout varies by aircraft, both type and (specific) airframe. However, the instruments typically look very similar.
In an emergency like what you describe, most of what's in the cockpit is entirely superfluous! If you don't know what it is, and the pilot doesn't discuss it when asked what's important, it's probably pretty much safe to just ignore, as long as you don't touch it. I actually disagree with mmathis' answer that the attitude indicator is important; there are many aircraft that don't even have one. Most of GA is flown in what's known as VMC, or Visual Meteorological Conditions, under VFR, or Visual Flight Regulations. Basically, that's the same as in a car; you're (the pilot is) looking out the window, using terrain features below to navigate and the horizon in front to keep the plane level. VFR flight in good weather is not rocket science!
Even landing a functional airplane in good weather on a wide, long runway isn't rocket science.
The hard part of flying is handling the bad situations: equipment malfunctions, strong crosswinds on landing, poor weather conditions aloft (including IMC, or Instrument Meteorological Conditions), etc. Or when ATC asks you to do something like land and hold short thus reducing the runway length by half, then vacate the runway quickly before that 747 on your tail touches down...
The first thing you'd probably want to do is to make sure the pilot isn't slumped over any controls. Tighten their harness to keep them from falling forward and interfering with the instruments or controls. This may involve moving their arms or even legs. Don't hesitate to do so if needed. The plane isn't going to immediately fall out of the sky.
Where might I expect to find certain, key controls?
Most if not all will likely be either in front of the pilot, or in the center of the instrument panel (assuming a side-by-side seat configuration). With the exception of big planes, controls and instruments in front of the right-hand seat will likely be more for monitoring the health of the airplane than for actively flying it. Radios and navigation equipment may also be located on the right hand side.
How could I contact air traffic control?
Locate the radio (usually labelled COM or COM1, possibly VHF/VHF1, but this may differ depending on the type of radio installed and the type of aircraft you're in). It will normally have two frequency readouts, one "active" and one "standby" (or similar).
If the pilot was already talking to ATC, just press the transmit button and speak into the microphone. Speak clearly, speak slowly (but not overly so; about 100 words per minute is good), say "mayday" a few times followed by the call sign of the aircraft you're in if you know it, let go of the button and see if someone responds. If not, try again once or twice. If still no response, set the radio to a frequency of 121.5 (MHz), set that frequency as active, and make the same transmission again. Exactly how to do this will depend on the specific radio; the pilot can show you before departure how to change the frequency.
121.5 MHz is the international emergency frequency and is monitored by ATC at all times. It is also monitored by aircraft able to do so. You will be able to reach someone on 121.5. Worst case it'll only be another aircraft, but they can relay to ATC.
As soon as you reach somebody, tell them that you are not a pilot nor a student pilot. This information is critical for them to best help you. You could say something like "I am not a pilot. Negative flight experience.". ("Negative" here means "no", not "below zero".)
Don't worry about what exactly to say. Just try to speak normally and describe the situation. ATC will ask for any details they need to help you, or for clarification if they need it. If you don't speak the local language, it's safe to say that all air traffic controllers internationally speak English. Don't make overly long transmissions; I'd say more than 20 seconds or so at a time is on the long side.
Once ATC knows about your situation, they will do everything they can to direct any other aircraft out of your way, as well as help you out in any other way they are able to. Don't hesitate to ask them for anything you feel that you need which they might be able to provide, including your position or the direction in which you should be flying.
What kind of terrain should I aim for, if possible?
No, seriously. It's always easier to set down an aircraft on a clearly visible runway than to do an outfield, or even a soft field, landing.
Failing that, any large, flat terrain clear of obstacles will do for landing in a pinch. Beware of ditches, fences and power lines! Especially if you're attempting to land somewhere that is not an airport, always make sure to tell ATC what you're doing so that they can direct emergency services your way.
What rate of descent is too dangerous?
While still in the air, that isn't a major concern. While headed for a runway, there really are only two important things to keep in mind. First, don't fly into terrain. Second, don't hit the runway too hard and too fast. If you're unsure, it's better to level off, or even "go around" by adding full power, climbing to altitude, and making a wide half-circle for another attempt. (Again, I'm assuming here that there are no problems with the airplane.)
If the runway is equipped with PAPI (precision approach path indicator) lights, that's a big help, as you can just descend at a rate that keeps two lights red and two lights white. If more than two lights are white then you increase your rate of descent; if more than two lights are red then you level off.
The only part where the rate of descent is going to make a lot of difference is during the last few dozen meters or less above the runway. This is where you flare (raise the nose of the aircraft). The flare serves several purposes: (a) it reduces your speed from flying speed to below flying speed; (b) it ensures that the main wheels touch down before the nose wheel; (c) it arrests the descent, and (d) it transitions the airplane from flying in the air to rolling on the ground. A really well executed flare can transition the airplane from flying to rolling almost imperceptably, but the odds of a complete novice managing that seem near zero.
If you raise the nose too much during the flare the airplane will start climbing during the flare while losing speed. If you're too high at the top of the flare, the airplane will drop hard onto (hopefully) the runway below. If you're too low at the top of the flare, you won't have time to arrest the descent (resulting in a hard landing) or the nose wheel may contact the runway before the main wheels. If the nose wheel touches down first, there's a very high probability of losing control.
How to deploy landing gear? (What might this button look like?!)
Have the pilot point it out to you. Most small aircraft don't have retractable landing gears, so this may or may not even be an issue.
If the airplane you're flying does have retractable landing gear, note that (a) you can't deploy it while flying too fast (there should be a plaque next to the control indicating maximum speed at which it can be deployed), and (b) once deployed, it will increase the drag of the airplane, so you'll need more engine power to maintain speed or rate of descent.
How to control the aircraft speed, and how slow is too slow?
Engine power is controlled by the throttle. Speed is controlled by a combination of engine power and pitch.
There is no single number for "too slow", even for a specific airplane, but assuming you're flying gently, not doing any abrupt maneuvers, it should be good enough to keep the airspeed well within the green arc on the airspeed indicator. When coming in to land, keep the airspeed near the faster end of the combination of the green and white arcs. This won't be exact by any means, but it should be good enough that you won't seriously risk breaking anything important.
Assuming a fixed power setting, the airplane will fly slower when you raise the nose, and faster when you lower the nose.
Assuming a fixed pitch and starting at level flight, the airplane will (eventually) climb when given more power, and descend when given less power.
Hence the saying "power for altitude, pitch for speed". Especially during landing, this is the opposite of what is likely to feel natural! It certainly took me a number of times to internalize that if you're too low on the final approach to the runway, the last thing you want to do is raise the nose! (I knew it intellectually, but it's quite another thing to actually internalize so that the correct response becomes second nature.)
How might I determine a good angle of attack?
Just fly level. As long as you are well above the surrounding terrain, just keep half an eye on the vertical speed indicator, keep it right around zero until you've found a landing site, and you're basically golden.
Angle of attack is important, but not for the kind of flying a passenger might do following pilot incapacitation.
No, you didn't actually ask this one, but it bears saying: Probably the most important maneuevering you might do in such a situation is to stay well away from clouds. There's a number of hazards involved with clouds, and the easiest thing to do is to just steer clear of them. For one, mountains have been known to hide out in clouds...
Also, never forget to fly the airplane first and foremost. Keep it in the air, and keep it away from terrain. Everything else can wait. If ATC asks something, you can always just tell them to "stand by". Just let them know when you're able to talk to them again.
So, to summarize:
- Talk to the pilot. Five minutes before start-up or departure to look over the cockpit can make this a lot easier.
- If something like this happens, then immediately tighten the pilot's harness, or otherwise make sure that they won't interfere with instruments or controls.
- The airplane isn't going to immediately fall out of the sky. You do have time to breathe.
- Don't worry about all the extra stuff in the cockpit. It's probably safe to ignore in the situation you're in.
- Landing a functional airplane on a large runway in good weather isn't rocket science.
- The most important instruments and controls will likely be in front of the pilot's seat.
- Saying "mayday" on 121.5 MHz will get you attention from air traffic control, as well as other aircraft in the area. Once you have their attention, they will do whatever they can to help you. Tell ATC up front that you're not a pilot.
- Aim for a runway, if at all possible. If you can't, then aim for flat, open, unobstructed terrain.
- Don't worry too much about the particulars. Fly level and stay away from terrain.
- Add power if you need to climb; reduce power if you need to descend. Push the yoke or stick forward to go faster; pull it toward you to go slower.
- Keep the airspeed indicator well within the green arc.
- Avoid clouds. They are not your friend.