So you know absolutely positively nothing about photography
Cellphone cameras are fucking great. I love them. I love the ability to take photos whenever and wherever at basically zero cost.
Point-and-shoot cameras have always been awesome and accessible devices.
This is not a post shit-talking "basic" cameras. This is a post for people who have only ever used basic cameras who want to know at least slightly more about photography.
Because, the thing is, a remarkable amount of photography is math. And if you don't know it's math, it looks like a mystery. And you may be standing there snapping a photo with your phone that looks pretty good, but your friend with a DSLR looked at the sky, twisted a dial, and took three steps to the left and they took a photo of the same subject that looks like it belongs on a magazine cover.
If you've come into possession of a DSLR camera and are disappointed that the photos you're taking aren't looking like the photos you thought came from DSLRs, I'm here to tell you about the math you may not know about.
At its most basic, a photograph is the result of light on a sensor. Let's consider a pinhole camera for a moment. A pinhole camera is a lightproof box with a piece of photographic paper on one side and a tiny hole in the other.
When you create a photo with a pinhole camera, you're using pretty much all of the math you would in a big fancy camera, just in a cruder form they are:
The sensitivity of the paper, film, or camera sensor to light (this is your "ISO" if you're using a digital camera or film). Light sensitivity can be easily changed on a digital camera, but on chemical-treated paper or film the sensitivity is predetermined and cannot be changed. If you want to change the ISO on an analog camera, you need to change the medium that's being exposed.
An opening to let light in - your F-stop, or aperture. The F-stop of a photo is how wide open the lens is to let light onto your film or sensor. In a pinhole camera, you have something that is theoretically a very very large F-stop because you have a very, very tiny opening to let light through (F-stops run in reverse - the bigger the number, the smaller the opening).
Exposure - your exposure is the amount of time you leave your sensor open to the light. The majority of photos you see in the world have exposure times that are measured in tiny fractions of a second, sometimes in thousandths of a second. If you're using photo paper in your pinhole camera, you may have an exposure time of minutes rather than tiny portions of a second, but your photo exposure will still depend on how long you want to leave your "lens" open.
Focal length - your focal length is a description of the relationship of the distance between the light source and the light sensor. You can manipulate this in a pinhole camera by making the camera longer or shorter. A larger focal length means a narrower field of view - it zooms in on the subject.
A pinhole camera is the simplest camera that lets you, the photographer, control all of the elements of a photo. This is, functionally, fully manual photography.
So what's the difference between all that and a cellphone camera?
Point-and-shoot cameras like those on cellphones give the user more limited control over these settings. For instance, think of a disposable camera. On a disposable camera, the photographer has control over one setting - the ISO of the film, which they can select at purchase. They can't control how wide the lens opens or how long it stays open, and the only way they can compensate for lighting that is a poor match to the ISO is flash.
Cellphone cameras are very much like a standard point-and-shoot. By default, users point their cameras, then shoot a photo. Many cellphones have a "pro" mode that will allow the user to emulate different ISOs or f-stops, but the sensors in cellphone cameras aren't as good as the ones in camera-cameras, and the lenses are very limited as well. Some cellphone cameras and point-and-shoot digital cameras WILL allow users to set longer exposures, and many cellphone cameras have multiple lenses which does allow for some lens effects, but they don't give a huge amount of control to the user.
Okay so let's say I've got my new shiny camera, what do I need to know?
For best results, you want your ISO to match the light you're shooting in. Low ISO is for bright light, high ISO is for low light. If you wanted to take snapshots of your family outdoors at disneyland in the summer, you'd buy 100 ISO film. When I used to shoot football games at night in oddly lit stadiums, I'd use 1600 ISO film. If you have a DSLR camera, there's a setting somewhere in there that tells you how to set the ISO.
If you are shooting in relatively low light and the photos are turning out darker than you'd like *but* things are moving too quickly to use a longer exposure, you can bump up your ISO for brighter, sharper images but they will be more noisy and grainy than ones shot at a lower ISO. If you want clean, smooth, crisp images, your goal should be to shoot with the lowest ISO possible.
The Aperture of your camera lens determines your F-Stop. This acts like the pupils of your eyes. When it's really really bright out, your pupils shrink down to let in less light. When it's darker out, your pupils get bigger to let in more light. If you are shooting in low light, you want a low F-Stop, which means that your camera's lens is open really wide. If you are shooting in a bright environment, you want a higher F-Stop, which will mean the opening is very small.
Since your F-stop interacts with the focal length of your lens, you will find that zooming in with the lens often makes images darker. To shoot clear images from far away, you need to be very conscious of your F-stop, your ISO, and ambient lighting conditions.
Exposure describes the length of time you set the camera to leave the aperture open. In many DSLRs this can span from 1/3200th of a second to infinitely long (the "bulb" setting means "aperture is open until you close it.") If you want sharp images of frozen motion, you want the fastest speed that you can get. Sports photography and photography of things like insects or milk crowns often use extremely short exposures to get sharp images. If you want blurry images you want slower speeds. If you want to take a photo in a low-light environment and capture motion within that environment - for instance, taking photos of cars on a freeway at night - you want slower speeds (if you want to do this in a brighter environment, like taking photos of a stream in the daytime, you want slower speeds and a specific kind of lens filter called a neutral density filter). When exposures are set to be longer than about 1/60th of a second, images with motion start to look blurry.
Focal Length determines the field of view of your subject. If you have a lens with variable focal lengths, this is called a zoom lens. A longer focal length zooms you in and a shorter focal length zooms you out. Lenses with fixed focal lengths are called prime lenses, and can't zoom in or out.
Depth of Field - your depth of field is a combination of the interaction of your focal length, your distance from your subject, and your F-stop. The depth of field describes the relative amount of space in a photograph that is in focus. A long depth of field means that much of the image plane is in focus. A short depth of field means that a narrow portion of the image plane is in focus.
A low F-stop produces a narrow depth of field. A long focal length produces a narrow depth of field.
You can think of your camera as a tool that measures time and space. Your ISO and Exposures are measurements of time (how quickly the sensor senses the light, how long the sensor is exposed to the light), the F-Stop and the focal length are measurements of space (how wide the aperture of the camera is, how far the lens is from the sensor).
The pre-set modes on your camera, the ones on the dial that show a person running, flower, or a cloud, or a lady with a hat - these are generic settings that combine an ISO, exposure time, and f-stop that are likely to work well for outdoor action shots, landscape photography, cloudy light, and portraits. When you're using those pre-set modes, you control the focal length and not much else.
When you understand that the running person/action mode means low-ish ISO combined with high shutter speeds, you can start just setting your own ISO and shutter speed when you're shooting sports. When you know that portrait mode sets you up for low-ish f-stops, relatively quick shutter speeds, and mid-range ISOs, you can just start setting those things on your own so you can have more control.
"What about light metering?"
Since your camera is a machine that records light, light metering is pretty important. The light meter of your camera will tell you if your settings are "correct" for the amount of that the light sensor senses. In most modern cameras there is a light metering display on the bottom edge of the viewfinder that goes from negative to positive; if the meter shows that you are in the negative it means that your photo will be under-exposed (too little light will get to the sensor and the image will appear dark), if the meter shows that you are in the positive it means that your photo will be over-exposed (too much light will get to the sensor and the image will appear too bright - "blown out"). The way to correct for under or over exposure is to change the length of the exposure, making it longer for underexposed images and shorter for overexposed images.
What the light meter is doing is thinking about all of your settings and the lighting for you. It looks at the ISO, focal length, f-stop, light hitting the sensor, and planned exposure time and tells you what that combination of settings is likely to produce - something too bright, or something too dark.
When you are more experienced with photography, you get good at juggling these things on the fly and messing around with them more, which is how you can do the magic of looking at the sky, twisting a dial, taking three steps to the left, and knocking it out of the park with a picture.
It only looks like magic because you're doing a ton of math under the hood that is extremely non-obvious to people who are new to photography.
Anyway, here is a good guide to depth of field and what goes into it.
Here is a basic photography textbook that explains the principles that I've gone over here in a lot more detail with a lot better explanations. It's a film photography textbook, but one of the cool things about photography is that a lot of stuff from the analog era is still relevant in the digital area, and the basics haven't changed.
However all of that is about the *technical* aspects of photography. Photography isn't just a record of exposure time and focal length, so here's a basic photo composition textbook that talks about the artistic principles of photography.