As you are looking for a campsite to reserve, for your upcoming summer vacation, try to be flexible with the site you'll accept. If you have certain requirements relative to the size, read the descriptions carefully on http://www.recreation.gov. You may reserve a campsite up to 6 months before your arrival date. Group sites may be reserved up to 1 year ahead.
Reservations typically run between mid-May through Labor Day; but that can vary by campground. When a campground is open outside the reservation period, the campsites are available for first-come-first-served customers. Even during the reservation period a portion of campsites are not reservable ahead of time. During the reservation period, if a reservable campsite is not reserved, it is available for first-come-first-served customers if you check with the on-site Host.
Generally, reservations are recommended for camping between the 4th of July and Labor Day.
If the site you want is not available, there are usually other similar sites in the same campground. You may also want to look in other, nearby, campgrounds.