Like many things, photography is a delicate balance between science and art. You need to master both to succeed.
Most people already have glimmerings of artistic sensibility — it's why they're drawn to photography in the first place. This is my quick essay on the technical basics. Learn these basics, and then you'll have a nice balance of art and science at your fingertips.
Someone who shoots and hopes is taking a picture; someone who deliberately mixes art and science is making a picture. Be a maker, not a taker!
Exposure is how much light hits your sensor. If it hits for too long, your picture is overexposed and blown out; if it's too short, your picture is underexposed and too dark.
It would seem, then, that one should simply let the camera determine the optimal exposure, right? Absolutely. Cameras can make pretty good guesses most of the time — that's what 'automatic' modes on cameras do. But we don't want to rely on guesses. We want to be in control.
The problem is that there are three variables that control the exposure, which means there are a near-infinite number of ways to get "correct" exposure, and the end-results all look different.
The three varibles are:
ISO refers to how sensitive your sensor is to light. It comes from the old days of film — "ISO 200" was best for outdoors, whereas "ISO 400" was twice as sensitive and better for indoors. Nowadays, digital cameras emulate light sensitivity on the same scale. Instead of having to shoot an entire roll of film at one level of sensitivity, you can now tell your digital camera to have a different level of sensitivity whenever you want.
ISO ranges from 100 up into the thousands. On a practical level:
100-400 is best for sunny outdoors. 400-1200 is best for indoors. 1600 and up is for very low-light situations.
The danger of increasing ISO is that the picture gets more grainy as it's turned up. You start to see weird artifacts in the pictures. The darker it gets, the harder it is for your camera to distinguish signal (light) from ambient noise (heat). That's the tradeoff: in return for working in darker situations, you start to lose picture quality.
Low light, ISO 1600... came out too grainy!
Aperture is the size of the lens' hole. The bigger the hole, the more light gets in. Aperture is measured in units called "F stops" (or just "stops of light"), and written as "f/8". The smaller the f-stop number, the wider the hole (which seems weird at first.) Each lens has its own intrinsic aperture range.
f/1 - 2 : super big hole f/3.5 - 5.6 : pretty big hole f/5.6 - 8 : the 'sweet spot' for most lenses, where things usually look best. f/8 - 11 : somewhat small hole f/11 - 22 : approaching pinhole sized
Why does aperture matter? Because the bigger the hole, the shorter the depth-of-field.
Depth-of-field is how much of the picture is in focus. If absolutely everything is in sharp focus (foreground subject, background), then it's a "high depth of field". If only a tiny bit of the subject is sharp and everything else is blurry, then it's a "shallow depth of field".
Artists like to mess with aperture directly, because depth-of-field is an artistic choice. For example, a portrait with the background blurred feels very different than a portrait where you can see every detail behind the person. For a blurry background, you'd choose f/2. For a sharp background, you'd choose f/11. If you go beyond f/11, you may start to lose image sharpness due to a phenomenon called diffraction.
Lenses with big apertures cost a lot of money, because they allow you to work in lower light, and give you bigger choice in depth-of-field (artistic choice, that is.)
(For more info on depth-of-field, see this article.)
Wide aperture (f/2)
Small aperture (f/8)
The shutter speed is how fast the hole opens and closes to expose the light sensor.
Assuming the ISO is held constant, shutter speed and aperture "trade off" with each other. That is: if the aperture is huge, then the shutter speed needs to be really quick to avoid overexposing. If the aperture is tiny, the shutter needs to be open for a while to avoid underexposing. Changing one variable usually changes the other.
Shutter speed is measured in fractions of a second. The main effect shutter speed has is on blur. For a handheld shot, humans generally need the shutter speed to be 1/60th of a second (or faster) to avoid the whole picture being blurry from shaky-hands. If you use a tripod, this restriction is removed. Of course, this doesn't stop the subject from moving. :-) Then again, maybe you want the subject to be blurred as an artistic choice.
High speed (1/1250 sec)
Slow speed (1/20 sec)
Here is the basic algorithm of the clueful photographer. With practice, this technique becomes second nature.
Of course, in a given situation you may decide that subject blur is more important to you than depth-of-field. In that case, set the camera to "shutter priority mode" (usually letter "S" or "T" on the dial) and repeat the algorithm — this time you get to set the shutter speed, and decide if the proposed aperture is acceptable.
If you're really hard-core, you can put the camera in full manual mode ("M" on the dial), where you get to choose all 3 variables. The camera will warn you if your over- or under-exposing, but it's your own artistic choice to make.
One more important variable to learn about! This last variable to learn has nothing to do with exposure. It has to do with the "zoom factor" of a lens. When you look at a scene, how much of it gets framed by the camera?
The classic camera lens uses a focal length of 50mm... because it's closest to the amount of scene that a human eye sees. It's considered the most natural — that is, the sizes of objects angles are closest to what our eyes see every day. Focal lengths that are bigger (100mm, 200mm, ...) are "zoomy", in that far-away things fill up the whole frame, and smaller focal lengths (28mm, 18mm, ...) are considered "wide angle".
Wide-angle is fun for outside panoramic shots, but beware that things start to get curvy and warped like a fishbowl. You may not notice in shooting landscapes, but indoors it will make rooms looked warped. And if you take a portrait with a focal length less than 50mm, it's extremely unflattering — it makes the face look warped and wide.
Zoom lenses are fun too, because it allows us to be lazy and not get too close to the subject. They're also flattering in portraits, as they have the opposite effect of the fishbowl — they tend to "flatten" things out. The effect is incredibly flattering for portraits. The ideal focal length for portraits is often considered 80mm, but models on magazine covers are often shot with 200mm or 300mm lenses, with the photographer standing 50 feet away!
High zoom (200mm, standing far away)
"Single lens reflex" (SLR) cameras and "Mirrorless" cameras are the big things you see photographers carrying. They have large sensors and interchangeable lenses.
For an SLR, when you look through the viewfinder, you're actually looking down and out through the lens... by using a built-in prism and mirror to bend the light, sort of like a periscope. When you take the picture, the mirror and prism need to "flip" to get out of the way, making that satisfying clicky sound. For a 'mirrorless' camera, you're watching a live video stream of whatever's coming in through the lens and hitting the sensor (just like when you take pictures with your smartphone.)
So why do serious photographers prefer cameras with interchangeable lenses, as opposed to point-n-shoot pocketable cameras, or just using their smartphones?
The bigger the sensor and bigger the lens, the better the picture quality. This is a fact of physics. For example, no matter how great the software is on your mobile phone (or how many 'megapixels' it has), the pictures will almost always look so-so... it's a pinhole lens and tiny sensor. By using a larger sensor and larger lens, much more light (information) is coming in, creating huge potential for superior images. Is it impossible to take a great photo with a smartphone? Not at all. But on average, bigger lenses and sensors are more likely to give you better-looking photos much more often.
I don't want to knock smartphones completely. They compensate for their small lenses by taking multiple shots and then using software to combine them into a single image that appears sharper than any of the originals. It often comes out pretty nice and is 'good enough' for most people, especially given the convenience of always having the device in your pocket!
BUT: if you really want control and high-quality, then it's worth using the bigger camera.
Once upon a time, 35mm film was the professional standard. All focal lengths are interpreted against this standard. In other words, a 50mm lens' framing ability is judged by the way it projects light onto a 35mm rectangle of film.
It turns out that making digital sensors (CCDs and the like) is insanely expensive, and thus a majority of digital cameras have light sensors that are considerably smaller than a 35mm piece of film. No problem, except that this means that a 50mm lens no longer gives the same look when projected onto a smaller sensor. The smaller sensor only picks up the cropped center of the image, creating an "effective zoom". It's not really zooming on anything, but because you only see the center part of the projection, its as if you were using a zoom-ier lens.
Most digital SLRs and Mirrorless cameras have what they call crop sensors. They have a 1.6x zoom factor. In other words, if you attach a 50mm to crop-sensor camera, it actually behaves like an 80mm lens.
If you're loaded with cash, you can spend $2-3k on a camera with a full frame sensor — one which is actually the size of a piece of 35mm film. Lens focal lengths will then be true. (The image quality is much nicer as well.)
On the other hand, if you go with a regular crop-sensor camera, I'd recommend buying a 30mm lens, since the result will be about 50mm.
Canon and Nikon own 95% of the SLR market, split it evenly, and have essentially identical products up and down the line. Neither is really much better or worse. Some argue that Canon has better UI, and Nikon has better sensors, but it's all debatable.
The important thing is to figure out which of your buddies are into photography, and whether they're Canon or Nikon people. Buy whatever brand your friends use, since Canon lenses only work on Canon bodies, and Nikon lenses only work on Nikon bodies. Then you'll always be able to test out, trade, swap lenses with your friends. It's a big deal... photography is a social hobby. If you buy an SLR other than Canon or Nikon, you'll forever be in an isolated minority.
In the realm of mirrorless cameras, Sony seems to be way ahead of everyone else. They have an "A7" (Alpha 7) line of cameras that use full-frame sensors, and are half the size and weight of DSLRs. It's what I use myself!
Specific camera bodies aren't that important. Bodies range from $600 to $3000, but the differences aren't that interesting. They're all greater than 15 megapixel resolution, and 15 vs 22 vs 50 megapixel is mostly meaningless — they're all able to create wall-sized posters. :-) When you buy a high-end camera body, you're paying for a nicer UI (bigger rear screen, nicer controls, fewer awkward on-screen menus, etc.) as well as a bigger light sensor. And as we discussed above, the bigger the sensor, the clearer the image. But the quality difference between a "crop sensor" (what most DSLRs have) and a "full frame sensor" (actually the size of a 35mm piece of film) usually isn't worth the $1500 price difference. If you're on a limited budget, it's way better to put your money into a fooi lens.
(Whatever body you buy, be sure to try it out in a store. Ergonomics are important! If it doesn't feel good in your hand, don't get it. It's a tool that should feel good to use.)
Remember this: lenses are everything. By buying a $400 lens (instead of using the cheap $80 lens that comes with most cameras), the difference in picture quality is just staggering. If you jump up to a $1200 lens, the quality of your photos really does jump by 3-5x. And you typically get a wider aperture (e.g. f/2.8) which means more beautiful depth of field.
My recommendation to beginners: buy a decent body (maybe even last year's model, used off ebay). Put all your money into a high-end lens. You'll be delighted.
Yes, this is a critical thing!
In fact, I believe that about half of photography is taking an artful photo, and the other 'half' is develping the photo artfully. This was true back when I used darkrooms as a teenager, and it's still true, but now we all use either Photoshop or Lightroom to develop digital photos. You MUST learn to use these programs, or you're basically ignoring half of being a photographer. :-)
Photoshop used to be the only program, but Adobe made a 'photographer centric' version of it called Lightroom, which is basically the same program, but optimized for developing pictures. If I want to cut out the head of a cat and paste in on a dog, Photoshop is best for that. If I want to manage all my photos and change the color, contrast, brightness, etc., then Lightroom is best for that. If you're trying to get into photography, put your time into learning Lightroom.
The only bad news here is that these programs are only available via a subscription. You get both together from Adobe, but you have to pay them $10/month, sort of like Netflix. It's annoying, but $120 a year is totally worth it considering how much money you've spent on cameras and lenses. This software is truly the other half of being a photographer, and in the larger picture, it's much cheaper than the first half. :-)