Keeping your firearm clean isn't just about making it look pretty; it's a safety issue. Although some guns are more tolerant of dirt and fouling than others, all guns need to be cleaned after use. That said, the AR-15 platform seems to be one of the more "picky" firearms in terms of requiring regular maintenance, so it's particularly important to keep "America's Rifle" clean.
In this video, Shooting Illustrated's Jay Grazio (and his magnificent beard) walk you through the step-by-step process of disassembling, cleaning, lubing and reassembling an AR-15. Of course, this guide is secondary to the owner's manual you received when you purchased your AR-15. If you no longer have it, most manufacturers will be happy to either send you a new hard copy or allow you to download a .pdf file (or both).