Shutter speed, ISO, and f-stop are the three variables you can control in the camera to adjust exposure. Changes in one can be offset by changes in another to keep the same exposure. However, changes in each of these three parameters have different influences on the look of the overall picture, even with the resulting exposure held constant. To make good tradeoffs, it is important to understand what each of these are and do.
This is pretty much what it sounds like, which is how fast the shutter opens and closes. Shutter speed is measured by the length of time the film or sensor (I'll use "sensor" from now on for simplicity, but that also applies to film unless explicitly stated otherwise) is exposed to the image. This can also be referred to as the "exposure time".
Typical shutter speeds for ordinary uses are from about 1/30 second to about 1/1000 second.
Slower shutter speed lets more total light hit the sensor, but higher shutter speed freezes motion.
1/1000 second is fast enough to freeze most motion in most cases. Such a fast shutter speed might be necessary for sports action, for example. However, the lower amount of total scene light hitting the sensor must be compensated for in other ways, such as higher ISO or wider aperture (see below). Those come with their own tradeoffs. There is no free lunch.
Note that motion doesn't only come from the scene, but also from movement of the camera during the exposure time. No matter how steady you try to be, there will be some motion whenever the camera is hand-held. As a result, there is a lower limit on shutter speed for hand-held pictures. 1/30 second is usually a good limit for hand-held shots with medium lenses.
Long focal lengths require shorter exposure times. Slight changes in camera orientation result in larger movement of the scene at longer focal lengths.
The F-stop is a measure of how much light from the scene the lens itself captures and projects onto the sensor. This is also sometimes referred to as the "aperture".
The amount of light a lens lets thru comes from the size of its optical opening. Consider two lenses, one with a 10 mm diameter opening and another with a 20 mm opening. The second will let four times as much light thru because a 20 mm diameter circle has four times the area of a 10 mm diameter circle. The light-passing quality of a lens goes with the square of its diameter.
But, there is another factor to consider, which is the focal length of the lens. Longer lenses (greater focal length) project the same scene larger on the sensor. A 100 mm lens, for example, projects the same scene twice as large in each dimension as a 50 mm lens. Since each dimension is twice as large, the same scene is spread over four times the area. This means that for the same amount of light thru the lens, that light is spread over a larger area for a longer lens. All else held constant, the brightness of the projection onto the sensor goes down with the square of the focal length.
The above two issues require a lot of mental math to figure out how bright the scene projection is on the sensor. Wouldn't it be nice if there was a normalized way to describe that across different lens focal lengths and diameters?
Yes, and that's what f-stop numbers are. We saw that the brightness on the sensor went up with the square of the lens diameter, but down with the square of its focal length. If we take the ratio of the two, we get a single value of projection brightness. This is exactly what f-stop numbers are.
F-stop numbers are the ratio of the lens diameter to its focal length. These are written as "f/xxx", like f/4, f/5.6, f/8, etc. This is essentially the normalized diameter of the lens. The "f" part stands for the focal length. For example, a 100 mm lens at f/4 has a effective optical diameter of 25 mm.
The nice thing about f-stops is that they work the same across different lenses. For example, f/8 will give you the same exposure whether that's from a 200 mm lens with 25 mm aperture, or a 80 mm lens with 10 mm aperture.
So why the strange numbers like f/5.6, f/11, etc? Remember that projected scene brightness goes up with the square of the aperture, and down with the square of the focal length. This means that exposure goes with the square of the f-stop. For example, f/4 causes four times the exposure as f/8.
Four times is rather a large jump. In photography, we usually think of factors of 2 as "increments". To get a factor of 2, the f-stop must be multiplied by the square root of 2.
The common standard f-stops come from starting at f/1, and dividing by the square root of 2 for each subsequent stop. Therefore, we get the progression
f/1, f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22
You usually won't see f/1 or f/1.4 except in specialty (and expensive) lenses. It's hard to make a lens that is as wide as its focal length, and still maintain a sharp projection.
Larger apertures let more light thru the lens, but also decrease depth of field. That's the range of distance from the camera where scene objects will be reasonably in focus.
At really small apertures, diffraction starts to matter. This makes the image less sharp. Light rays passing very near a physical obstacle bend a little around that obstacle. This always happens at the edges of the aperture, within about a light wavelength of the edge. For small apertures, more of the overall area is within this small distance to the edge, making diffraction relatively more prominent.
Diffraction is why variable apertures don't usually go past f/22 or f/32. The decrease in sharpness at smaller apertures would be too noticeable.
Another tradeoff is that the non-ideal characteristics of the lens become more apparent at wide apertures. Designing a lens is a whole set of tradeoffs of its own, with compromises inevitably made. Effects like chromatic aberration, non-uniform focus, edge distortions, and the like are always present to some degree. The larger the lens diameter, the harder it is to minimize these problems. These effects are therefore usually more pronounced at the widest-open f-stop or two.
ISO is a measure of the sensor (or film) sensitivity. Higher ISO numbers mean that you get more signal (or film density) for the same amount of light.
Making films more sensitive usually meant larger grains. There was therefore a tradeoff between grain noise and sensitivity. However, there were other tradeoffs too. Simply stating that ISO went with grain size is incorrect, or a gross oversimplification at best. There were tradeoffs that could be made in processing between maximum contrast and ISO, and different chemistries allowed for different tradeoffs altogether. For example, Kodak's famous Kodachrome film wasn't based on grain at all.
Modern cameras use electronic sensors instead of film. The sensor is a fixed part of the camera. You can't change the sensor to get different ISO values like you can with film. However, since the sensor signals are electrical, they can be manipulated with electronic circuits to provide an effective range of ISO values.
The native ISO of a sensor might be 200. The raw signals from the sensor can be amplified by 4, for example, to result in effective ISO of 800.
There are limits to this. All signals have some noise on them. The more the sensor signals are amplified, the more the noise is amplified too. The ISO limit of a digital camera is not how much the signals can be amplified electrically, but how much noise in the final image can be tolerated due to the amplification.
High ISO settings effectively give you more light to work with and allow more flexibility between the shutter speed and f-stop settings. However, too high ISO adds noise to the image.
How much the noise matters depends on how the image will be used. If it will be shown 1:1 pixel to pixel, then any noise will be seen directly. However, if the image will be shrunk to a lower resolution, then multiple original pixels will be "averaged" to make each final pixel, and random noise will be reduced. For example, if your camera takes 4200 x 2800 images, but you only want to show the result as a 1200 x 800 picture in a web page, then you can tolerate a higher ISO setting than if you want to make a poster of the original that people can walk right up to.
Physically larger sensors with less noise (allowing higher ISO settings) cost significantly more to make. A better sensor is one of the main features that makes high end cameras more expensive.
Manual versus automatic
Long ago, simple cameras gave you manual settings for the f-stop and shutter speed, and the rest was your problem. This is where common rules of thumb for exposure came from.
One example is the "sunny 16" rule. For a normal scene in sunlight, you get good exposure at f/16 and the shutter speed set to 1/ISO. For example, with the old Pan-X film that had ISO of 125, good exposure would be f/16 and 1/125 second. Of course you can trade off f-stop and shutter speed from there, like f/8 and 1/500 second, f/22 and 1/60 second, etc.
If it wasn't fully sunny, you'd adjust accordingly. Hazy sun was 1 f-stop down (factor of 2 less light). Cloudy bright was 2-3 f-stops down.
After a while you got reasonably good at judging this, but there were always some shots that were over or under exposed. If you were in doubt, you'd use a separate hand-held light meter. That would measure the scene light, and you'd previously set it to the ISO of the film you were using. The light meter then showed you a range of shutter speeds with corresponding f-stops that would work well.
Nowadays, pretty much every camera has a built-in light meter. Not only can it tell you what shutter speed and f-stop combinations would be good, but since everything is computer-controlled, it can go ahead and actually make the settings for you. With digital cameras, the ISO setting is also under computer control, so the camera can pick all three of shutter speed, f-stop, and ISO for you automatically.
But wait, do you really want the camera to make all the tradeoffs? How does the camera know you are taking sports action pictures and want fast shutter speed, and are willing to put up with less depth of field and/or more noise to get it? What if nothing in your scene is moving fast so that slower shutter speed is fine, but you want a large depth of field? What if you don't know from f-stuff and all that ISO-shmiso babble and just want to take a few pictures already?
This is why there are a range of cameras from "point and shoots" that optimize for low intimidation factor and price, to pro models that give all the flexibility to the photographer when he (or she, not going to keep saying that) wants it.
Even the low-end point and shoot cameras have different "program" modes. Most likely there will be something called a "sports" mode. That will strive for fast shutter speed. Other mode names make the tradeoffs less obvious. You provide the high level guidance by choosing one of several program modes, and the camera still decides the details on the fly under the hood.
Even pros rarely need fully manual exposure mode. Probably the most common mode used in a pro camera is "aperture priority". That means you pick the ISO, then specify the aperture on the fly, and the camera picks the appropriate shutter speed based on the amount of light it measures. Shutter priority works the same way except that you select the shutter speed on the fly and the camera picks the appropriate f-stop.
On these cameras, there are easy to reach dials to make the setting, and the camera shows you what it picked in the viewfinder. This way the pro has a single dial to trade off shutter speed and aperture, and can see exactly what the tradeoff is. If he doesn't like the tradeoffs, he can usually change the ISO fairly easily.
I generally use my camera in aperture priority mode. A dial under the right forefinger selects the f-stop, and I can see the current ISO setting and the resulting shutter speed in text below the image in the viewfinder. Changing the ISO means holding in a button with my left thumb, and adjusting a wheel with my right thumb.