Well, the first "Seriously Fun Photography" class is all behind me now.
We learned that to control exposure, we need to work with three related elements: Aperture, Shutter Speed, and Sensitivity.
The f/stops to memorize are f/1.4, f/2, f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22. If you forget these, make two columns, and at the top of the left one write 1.4 and at the top of the right one write 2.0. Now double each number as you go down the column (rounding off when needed). Changing one stop lets in twice as much light (or half as much, depending on which direction you go. f/2 lets in a lot of light, f/22 lets in very little light. So if you took a picture using f/8 and it seemed a little too dark, you would switch to f/5.6. If you took a picture using f/8 and it seemed a little too bright, you'd switch to f/11.
The common shutter speeds are:
1/1000th of a second
-- As a rule of thumb, if you are moving and you're subject is moving, you'll want to be shooting at 1/1000th of a second to get a sharp picture.
-- If you are still but the subject is moving along, it would be good to be at 1/250th or faster.
-- If you and the subject are both relatively still, you can probably handhold the camera as slow as 1/60th, but slower than that and you'll get a soft picture because of camera shake caused by pressing the shutter.
-- At speeds that are slower, you'll need a tripod to steady the camera, and probably want to trigger it using the self-timer or a release.
-- Many decent cameras have higher shutter speeds, and these are very useful for action or sports.
Notice that the relationship of these shutter speed settings is also doubling (or halving) the amount of light that hits your sensor.
This is the ISO "speed" of a digital sensor or of film. ISO 100, 200, 400, 800, 1600 and 3200 are available on many cameras (but not all), and you should take some test shots with yours to find out if the higher ISO settings are usable or not. Figure out the fastest ISO speed you find produces acceptable shots on your camera -- you'll need to switch to it sooner or later. Notice that each ISO speed is twice as sensitive (or half as sensitive) as the next.
Then we decided to start applying our general knowledge about the relationship between apertures and depth of field. While we start to get the idea when we say "f/2 -- shallow depth of field and f/22 - deep depth of field" actually trying this out in with some real world shots is always a good experiment.
So we set up an experiment that can be repeated at home: set your camera on a table or a tripod, and in front of it arrange people or objects in a receding line. Put the first person or thing just 3 feet away from the lens, and have the furthest be at least 12 feet away. Now set the widest aperture you can -- I use a lens that goes to f/1.4 for this -- and focus on the closest person or object. You'll probably find that the people / objects behind that are out of focus. Now run through the whole series of aperture settings you have available (you'll probably want to be in "aperture priority mode" so that the camera sets the corresponding shutter speed for an acceptable exposure. Or you can set that yourself). Try this and compare each shot -- more and more will be in focus until you should be able to get everyone in focus.
Now, keep in mind there's one other factor here -- the focal length you shoot with. Usually the effect of getting a main subject in focus and the background out of focus is much easier to achieve if you use a lens of at least 50mm or set as zoom to 50mm focal length or a more telephoto setting.
Many photographers think that "telephoto lenses have shallow depth of field and wide angle lenses have deep depth of field" -- it turns out that isn't exactly true, but for pragmatic purposes it isn't a bad way to think. If the goal is a sharp subject and a blurry background -- grab a 90mm or set your zoom lens about there.
(For a discussion on why the wide focal lens = deep depth of field idea isn't precisely true, read Do wide-angle lenses give you greater depth of field than long lenses?.)
Another thing that comes up at this point: some lenses allow your camera to reach to f/1.4 or f/2 or f/2.8, but many times the "kit lens" zoom that comes with a DSLR or the zoom lens built into a compact camera will not go to that wide-open an aperture. And to further add to the confusion: many common lenses that go from 18mm to 55mm (or 70mm) let you go to f/3.5 when using the widest focal length (18mm) but only to f/5.6 when you are using the long end of the lens (55mm or 70mm). That's just how those lenses are built.
Now, once we know a technique to control depth of field -- go towards f/2 to get a sharp person, blurry background or toward f/22 to get subject and background both focuses -- we want to think about why we would do it. Well, it's that kind of control that lets us emphasize or deemphasize what a viewer sees in a photograph, so we want to master it so we can control our images. Need to photograph a person against a cluttered, distracting background? Use selective focus. Need to show that a person has kids but keep the emphasis on the person? Use selective focus to make the kids visible but de-emphasized.
So, from a technical standpoint, as we approach any photo situation we'll want to decide on an ISO setting, a shutter speed and an aperture. The three are interrelated and all use a doubling / halving system so it is easy to calculate how to change them when needed.