The Grand Canyon is one of the natural wonders of the world. The UNESCO World Heritage Site is located in northern Arizona, in Grand Canyon National Park, and is one of the most visited places in the world. Formed over millions of years and carved by the Colorado River, it is a place of which pictures cannot do justice. To appreciate it, you have to visit and just take it all in, the breathtaking view from the rim going as far as the eye can see. In places, the canyon is upwards of a mile deep, from the highest rim to the bottom of the canyon.
The two main ways to visit the canyon are the North Rim and the South Rim. The South Rim is more accessible and more crowded, the North Rim is more remote. From the south the most direct way to the south rim is to hit Highway 64 or 180 (both get you there) going north from Interstate 40. You can also get there by bus or train from Flagstaff and several other major cities. Unless you have a National Park Pass, it costs $20 per vehicle to get into the park ($10 by foot or bike must), and that permit is then good for seven days.
There is plenty to do in the park, including hiking, rafting, and other assorted tours in the canyon, and there are also campgrounds and hotels, but beware that during the busy season (summer) you will need reservations well in advance. If you simply want to marvel at the view, but stay away from the crowds, you can simply drive in, park, take your photos, and then be on your way (of course you have to still pay an entrance fee).
Although most people think of Arizona as being a hot desert climate, the North Rim of the canyon is near 8000 feet, and there can be heavy snow in the winter.