First off, here's one of those modern 'infographics' summarising how we convince the camera to approximate the thing we're looking at, in terms of the 'brightness' of the resulting image:
In this you can see
Possible settings for different subject brightnesses
How the settings can be juggled whilst maintaining the same 'brightness' in the end result
The underlying maths that makes it all work
The technical quality impact of ISO settings
The aesthetic impact of aperture and shutter speed choices
I'll expand on this here, which will start out a bit 'wordy' but by the end we'll see some example images that put all of this into practice. Feel free to skip ahead, some of this info is really very geeky...
You could quite happily get lost in a long discussion of photometric exposure if you so desired, but it would require a whole volume in and of itself to really get to the bottom of things; so I am keeping this simple.
The brightness of a scene is measured in Exposure Values (Ev). A dimly lit interior would be measured at Ev 0. Ev 1 would be twice as bright, Ev 2 four times as bright, etc... Ev -1 would be half as bright as EV 0.
Typically in photography we work in the range of around -6 to nearly 20 Evs. Although things can always get brighter, or darker in reality.
In this day-and-age we don't think much about absolute Evs because the camera does all of the work for us. It measures the Ev of the scene and, based on our chosen ISO setting, suggests appropriate aperture and shutter speed exposure settings.
It is enough to appreciate that there is a very definate (and mathematical) relationship between the brightness of a scene and the exposure and sensitivity settings that are appropriate to approximately reproduce the scene.
By definition, Ev 0 at a sensitivity of ISO:100 requires an exposure of 1 second at f/1. Which, we shall see, at a sensitivity of ISO:3200 is equivalent to an exposure of ⅛ at f/2.
There are tables of exposure values available (eg. subject lit by bright sunlight, Ev = 15) and it is possible to manually calculate the exposure and sensitivity settings required.
But we can let the camera do that.
However, we might not like the settings the camera suggests. If we can't trust our subjects to stay still for an exposure of ⅛ of a second in a dimly lit interior we may decide to try a shutter speed of 1/15th. But if we can't open the aperture any wider than f/2, we'd have to push the ISO up to 6400, despite the additional noise that will introduce.
Looking at the above infographic, we can see that if we move any of the settings downwards a given number of steps, we must consequently move the other settings upwards to compensate by the same total number of steps.
Each of these steps, of course, is one exposure stop.
In the bright sunlight example, we may decide that the depth of field at f/22 is too great. We would prefer to isolate the subject by throwing the background out of focus, which might be achieved by using f/8.
f/8 is 3 stops more than f/22 (8x more light passes through the aperture), so we may subtract 2 stops from the shutter speed and 1 stop from the sensitivity to compensate.
When shooting, we tend to do this by counting rather than calculating. Or else by observing the change in the 'exposure indicator', ensuring it returns to the same place it started from (usually the zero mark) after making the adjustments.
Well, we've been dealing with some pretty weird numbers and it must seems like they're unnecessarily complicated, or simply bonkers.
But they do have a rare beauty about them, which the maths of the matter reveals.
Whether we're looking at the exposure value of the subject brightness, the aperture and shutter speed of the exposure, or the sensitivity, we're concerned about one common, underlying, factor: the resulting brightness of the image.
If we halve the amount of light in the scene (leaving all else constant) then the resulting image will be half as bright. Similarly if we halve the shutter speed. Or halve the size of the aperture through which the light passes. Or indeed, halve the sensitivity.
So all of these things are related, and because of their respective weird numbers we can express that relationship mathematically:
Ev = log2(N2/T) - log2(S/100)
Let's take an example.
If the measured brightness of the scene is found to be Ev 0 (at ISO:100) then the combination of aperture, shutter speed and ISO setting should also be zero if the resulting image is to be a reasonable approximation of the scene.
So let's plug some numbers into the above equation: Aperture(N) f/2, shutter speed(T) ⅛ ISO(S) 3200.
N2 = 4
N2/T = 4 / 0.125 = 32
log2(32) = 5
S/100 = 32
log2(32) = 5
5 - 5 = 0
Okay, so let's look at our 2 examples for Ev 15 (subject lit by bright sunlight): f/22,1/125th, ISO:200 vs f/8, 1/500th, ISO:100. Does our formula show that these two sets of values equate to the same Ev (15)?
For: f/22,1/125th, ISO:200
N2 = 484
N2/T = 484 / 0.008 = 60,500
log2(60500) = 15.9
S/100 = 2
log2(32) = 1
15.9 - 1 ~= 15
For: f/8, 1/500th, ISO:100
N2 = 64
N2/T = 64 / 0.002 = 32,000
log2(32,000) = 14.9
S/100 = 1
log2(1) = 0
14.9 - 0 ~= 15
And the answer is, yes they do.
I think this is pretty magical, mathematically combining such disparate physical properties (aperture area, shutter duration, sensitivity gain)... They told me in school you can't add 5 apples to 2 pears; well, you can if you convert them both into 'fruit' (5 apples plus 2 pears = 7 fruit). This is what the log2 function does for us. It converts the different geometric scales into a simpler common arithmetic scale.
But enough of this! In practical terms the formula is of little day-to-day use. It does improve our appreciation of the various number scales in use, so we might as well be aware of it. Plus, it means I can completely forgive the aperture scale for being just so damn weird (even though I do like knowing my square-root-of-two-times-table).
If you want to know more, then just search t'internet for 'exposure values'.
ISO and Quality
Putting all of this into practice, this gallery offers 7 examples:
Isolating your subject with narrow depth of field at a wide aperture
Taking advantage of a wide depth of field with a small aperture
Creative motion blur using a slow shutter speed
Freezing movement with a fast shutter speed
Creatively overexposing for a high key effect
Underexposing for a low-key effect
Shooting at a high ISO in low light