HDTVs, by default, come set up to be put on display in a showroom. The settings are cranked up to the extreme, with vibrant and bright colors designed to catch your eye among a sea of TVs. While it may seem desirable, it doesn't provide for much of a cinematic experience and is not at all accurate to colors in the real world. This is why calibrating the TV can make it a much better experience overall.
The first thing to do is put the TV into "Movie" mode. This will get you about 70% of the way toward being properly calibrated. Movie mode is more muted, and has warmer color tones that are much more accurate. In fact, most people in most situations will probably find this step alone to be adequate for getting a more realistic picture.
If you'd still like to perfect your TV's settings, there are DVDs that can help. Digital Video Essentials HD Basics by Joe Kane is a great guide. It has visual tests to adjust brightness, contrast, color, gray scale and more. This DVD is $39.95. There are also more calibration options available for download on AVSforum.com..
The best (and most expensive) way to get your TV calibrated is to have a professional come and do it. He or she will be able to optimize your TV's picture based on the lighting in the room. He or she will also have professional tools to dial in the proper settings. This can cost at least $300, which is only worth doing for the more expensive high end TV sets.
After your TV has been calibrated, you'll have to allow yourself time to adjust to it. If you're used to watching a bright, almost neon-like picture, a properly calibrated display will look muted and dull. In time, however, it will look more natural and normal. The goal of calibration is to achieve a picture that is as close as possible to the reference monitors used by the director. It ensures that you're seeing exactly what the director had intended, instead of the blown-out, oversaturated colors that most TVs come set up with.