Each year, hundreds of couples get married at Grand Canyon National Park in Arizona. All weddings require a special permit from the National Park Service. They may be scheduled up to a year in advance of the wedding date. As of 2011, permits cost $175. See the website link for contact information.
Apply for a marriage license through the Clark County (Arizona) clerk's office. It is valid for one year.
Hire a member of the local clergy or public official empowered by the state, such as a justice of the peace.
Settle on a site and date. South Rim Shoshone Point, for example, has a few picnic tables and a fire ring. It is open for weddings, and may be reserved in advance.
For a wedding with a twist, there is the helicopter option. The helicopter can take the party below the rim to the Grand Canyon West Ranch, or a romantic vista overlooking the rim. The Grand Canyon Skywalk is another possible venue.