Quick Setup
The following are things to take into consideration when setting up your camera. These are just suggestions for getting the best quality, not photo-laws, so use your own judgment.

1.) Begin by using the highest image quality you can. This usually means Jpeg Large. You should also select the finest setting (may even be superfine) which may be text saying superfine, or a graphic showing a semicircle or a staircase icon; choose the semicircle indicating smoother.

The idea here is that you spent all that money on a gazillion megapixel camera so why not use all those pixels? Also, how large you can print an image and the quality are directly related to the amount of information you capture when you push the button, in other words, megapixels.

Since you never really know how you will use the image, take it as large as you can and reduce it later if you want. You can always make images smaller, but not larger.

2.) Select the lowest ISO. ISO will be explained later, but by selecting your lowest ISO, you are choosing the camera's true sensitivity to available light. This will result in better quality images. By default, this is set to AUTO.

3.) AUTO White Balance is fine unless you know exactly what kind of light you are shooting in, and even then the camera usually does an adequate job of setting the correct white balance.

4.) Turn OFF Digital Zoom unless you have some indication of when it is going between optical and digital zoom. Optical Zoom is the lens physically moving away from the sensor (the electronic noise and the moving lens). Digital Zoom is an algorithm that digitally crops and reassigns pixels resulting in lower image quality.

5.) Turn OFF Camera/Shutter Sound. It's really annoying, so keep it on if you must, but it makes covert photography difficult.

6.) Change your Color Space (Settings, Parameters) to Adobe RGB if you have the ability to do so. This is a more accurate, though less vibrant/saturated, range of color that the camera will capture. This will make printing at home easier. Keep it set to its default sRGB if you only print online. Turn off any color boost like Vivid Color.

7.) Turn Off the Date Stamp. This is the setting that puts an orange date across your image. Besides ruining your image, it is totally unnecessary since the date is saved in the file within its metadata (explained later).

8.) Locate and use your Exposure Compensation.
Exposure Compensation is one of the easiest ways to "over-ride" your camera's exposure settings. This is a better choice than changing your ISO, because it doesn't amplify anything, it just shifts your shutter speed and/or aperture settings, thus retaining your image quality.

Because the camera exposure meter can be fooled by tricky lighting situations, most cameras will have the ability to compensate for the camera's faults. Sometimes this is labeled EV or Exposure Compensation.

Usually it is easy to access (some even have a +/- button on the back, if not try your function button).

Basically by setting this, you tell your camera to over or under expose the scene by the amount you have set. This means that if you are having trouble getting the right exposure, you can fake your camera out. Just look at your LCD screen to decide if your image is bright enough.

Most camera's will have a couple other things to help with exposure such as a histogram and blinking colored areas showing areas of clipped detail.