It's Got To Be More Complicated
OK. So after reading for 10 minutes, it seems there are some basic rules to photography.
1. If you can spend $3000 on a camera, all subsequent rules do not apply, because your sensor is big enough that setting one doesn't have to sacrifice the other. Okay, just kidding.
2. Aperture, and Shutter speed are both ways of controlling how much light the sensor is exposed to.
3. Aperture controls depth of field. The higher the F-stop number, the less light is allowed onto the sensor, but the more of your picture will be in focus. Unless you're shooting something you specifically want a blurry background for, you should choose the largest F-stop number you can that provides adequate light. This way, the greatest portion of your photo will be the sharpest.
4. Shutter speed controls how long the sensor is exposed to light. A higher shutter speed should be used for moving objects. A slower shutter speed for situations with less light. You should use the slowest shutter speed you can that keeps your picture in focus and doesn't overexpose it.
5. ISO is how sensitive a sensor is to the light it is exposed to. Always use the lowest ISO you can, as you'll always get more noise as you increase the ISO.
Obviously, I'm missing something, because other people can take much better pictures with the same camera I'm using.
Specifically, I'm wanting sharp and vivid pictures.