How do YOU expose properly?

Sorry to say this, but your quesiton is just to broad for a reasonable answer... unless you can settle for "it depends" as a response. It depends a lot on the camera being used (capabilities), film being used, schedule, and environmental conditions.

To your list, also add: to quetion 1 - incident metering and guestimate (e.g. Sunny-16, etc).

For almost all subjects I use the matrix metering in my Canon DSLR. For most subjects I shoot and check a histogram, and adjust accordingly. For moving subjects, I usually shoot a preliminary shot and pre-adjust the compensation based on the histogram. When using spot metering, don't forget that the meter wants to set the exposure so that what's in the spot comes out as a middle tone: so you have to open up to make a bright subject appear brighter, and close down to make a dark spot darker. So the answer, then, is "it depends."

OK, an example. I googled the topic and got this photo.

Assuming the light is coming from a window upstairs, no flash, how would you meter and how would you expose? Let's assume you don't have time to check the histogram (because that's easy).

How would you reason, how would you estimate the scene, how would you make best use of the camera's light metering tools?

PER THE TERMS OF USE FOR PHOTO.NET: DO NOT POST PHOTOS THAT YOU DID NOT TAKE.

For maximum accuracy I use a spot meter; reading off both the brightest and darkest areas of the scene, as well as a dark area I want to retain texture in. This is basically an adaptation Ansel Adams's/Minor White's Zone System of exposure.

Aim camera or meter, push button, note reading, apply almost 50 years of experience and adjust camera setting. Works most of the time. :)

For the flash pic Charcoal Happy posted above, it is yours? Use an incident flash meter. If you are so foolish as to do attempt to do this with available light, incident meter reading, same meter you use for flash.

Note to above, hard to chimp with a film camera.

Well, the OP never stated film only, so chimping is a viable option in digital. You could bracket with film.

I personally, for a scene like this, bust out my light meter, walk over there, and measure the light, then set the camera accordingly.

After that, you need to judge the scene. If overall I think it's middle gray, I might do the entire frame, if I think it's pretty off to one side or the other, I will compensate as needed, or go into a "spot" mode. Maybe spot meter off of something, get the reading, then recompose. Seriously, outside of a studio, there is no one method to rule them all.

1° Which metering mode do you use: matrix, center weighted, center spot or spot?

None of those. I use an incident meter.

2° What exactly do you measure? The whole image, the brightest part, the darkest...? How do you determine what the darkest or brightest part is? Color can be misleading: a black shirt in direct sun will show up brighter than a white shirt in the shade.

The light shining onto the subject.

3° How much compensation do you dial in? I've found that the smaller the area measured (spot vs center vs matrix), the more I have to compensate.

None.

or you can simply walk over there with the camera and take a number of readings like one would use a meter, if I still had one.

1. Spot, always
2. I meter the part of the subject I want to appear middle gray in my exposure
3. It depends on the subject - obviously a completely dark subject or a completely white subject will need compensation

Metering for manual exposure is mostly a matter of experience. You quickly learn how to evaluate a scene and decide what parts of the scene should occupy what parts of the brightness range.

<Chas>