The exposure triangle* - three basic controls that affect each other, to create an exposed photograph.
The only reason we have any of these controls (aperture, shutter speed or ISO) is to change how light or dark the photograph is.
I will include a brief explanation to each control, but my focus is to highlight their creative uses. There are millions of great articles that explain what each control does for exposure of a photograph, and I don't want to retread old ground - there are lots of numbers and it's really boring.
Where do I start?
You have to decide what sort of image you want. Do you want the background blurry, or all in focus. Do you want the subject or background blurry, or not? Based on what you want, you'll know which settings to change.
Once you master this, you will begin to think how you want the photo to look before you change any settings. If you give me a scenario, I can tell you what settings I want before I even have the camera in my hands, and you'll get to that point, too.
1. Aperture (depth of field)
The smaller the f/stop number, the wider the aperture. The bigger the f/stop number, the narrower the aperture. A wide aperture (e.g. f/1.8, f/2) means a shallow depth of field, so everything leading up to where you're focusing is blurry, then that section is in focus, then everything behind that point is blurry.
Kinda like this bluebell:
See how everything infront and behind that flower is blurry?
That was shot on f/2.8. If I'd have shot that at f/11 or f/16 all the leaves before it and after it would've also been in focus.
That's not a bad thing, but I wanted the bluebell to stand out from the foreground and background, so I shot it at f/2.8 to get it nice and crisp.
Because I wanted a wide aperture (f/2.8) we'd then adjust shutter speed and ISO to make sure we're getting a nicely exposed image (so we can actually see what the photo is of).
Take these images of Saskia, they were shot at 130mm from f/2.8 to f/16 (see captions) and you can really see how aperture effects the resulting images. I shot this on aperture priority (I tell the camera what aperture I want, and it adjusts shutter speed to get the same exposure).
2. Shutter speed
Shutter speed is all about motion.
A short shutter (like, hundredths/thousandths of a second) will freeze most movement, (how far are you really going to move in a thousandth of a second? Probably not much, right?).
But a long shutter (tenths of seconds, or whole seconds) will capture more movement and cause blur -
If I get out of a chair, and you take a 1 second shutter, chances are I'll probably be stood up by the time that shutter finishes, so I'll be a blurry mess.
If I get out of a chair, and you take a 1/200 second shutter, chances are I'll have barely moved by the time that shutter finishes, and I will appear still in the image.
The same is true with other subjects, just look at the waterfall below.
So a long shutter makes all photos blurry?
No! You can get perfectly sharp images with REALLY long shutter times. All you have to do, is move in the same direction as your subject.
You want each part of your subject's light to hit the exact same pixels in your camera, so you just move with it. The Hubble Space Telescope does this - because space is really dark, it takes hours of exposure to get a photograph bright enough for us to see. Hubble moves with the spin of the galaxy to capture the stars in perfect sharpness.
ISO is how sensitive the image sensor or film is to light. ISO 100 is not that sensitive, it'll take a lot of light to expose the image. ISO 10,000 is REALLY sensitive, it won't take much light to expose the image.
ISO is our slave. We change aperture and shutter speed to fit with what sort of image we'd like, then change the ISO to make sure the photograph is perfectly exposed, (whether it needs to be more sensitive to make the photo brighter, or less sensitive to make the photo darker).
The only problem is... higher ISO = more noise. Noise is grain, and too much makes most photos look rubbish. It distorts the photo and detracts from what you're trying to photograph. Sometimes noise can be good - like gig and documentary photos, it just kinda looks cool.
But usually you want to keep it as low as possible.
If you learn to master these three controls, you'll be able to build a photograph before you even grab the camera. By knowing what your photograph to look like, it's much easier to create the end result, but it's only by practising with aperture, shutter and ISO that you'll achieve what you need.
*[Summary for those who don't know what the exposure triangle is: The exposure triangle is made up of three controls on the camera: aperture, shutter and ISO. Aperture controls the size of the opening in the lens, shutter controls how long light reaches the image sensor/film, and ISO is how sensitive the image sensor/film is to light.]