How to look
Much of what a first night under a dark sky misses is not in the sky. It is in the eyes, which take half an hour to become the instrument they can be, and in what a lit phone does to them.
The eyes take half an hour
The Park Service's stargazing tips put the figure at twenty to thirty minutes for the human eye to fully adjust to very low light. The anatomy behind it is the American Academy of Ophthalmology's: the cones, concentrated at the center of the retina, give color vision and fine detail; the rods, concentrated toward its edges, give vision in low light and to the sides, and are five hundred to a thousand times more sensitive to light. There are about 120 million rods to 6 million cones. The sky does not change during the half hour. The eye does.
Losing it
Bright lights delay the process, in the Park Service's words, and a white phone screen, a headlamp or a car's dome light is a bright light. NASA's advice names red lamps and red LEDs as the best lights for stargazing, because red light has the smallest impact on night vision. That is why the Park Service's tips ask for red lights only, and why every page on this site has the red toggle at the top. The apps page gives the iPhone's own path to a red screen filter.
Looking slightly to one side
The same anatomy is the reason for a habit observers call averted vision. A faint object looked at directly falls on the center of the retina, where the cones are. Looked at from a little to one side, it falls where the rods are, the cells hundreds of times more sensitive to light. The technique is not in the sources below; the anatomy that makes it work is.
Eyes, then binoculars, then a telescope
NASA's figure for the eyes is a view spanning 180 degrees, against the tiny patch of sky a telescope shows, and it names sights visible only to the naked eye: the constellations, lineups of the planets, and the arc of the Milky Way. Meteor showers, it says, are best experienced lying down and looking up.
NASA's answer to the question of the best first telescope is, often, a pair of binoculars, for their portability, their ease of use and their lower price. They show a wider area of sky than a telescope, an advantage for comets and for close pairings of the planets with the Moon, and they easily reveal star clusters, double stars, the four largest moons of Jupiter, and stars too faint for the eyes alone. They can be handheld, and they are a much more useful tool mounted on a tripod. A telescope is for the planets, comets, the Moon, and the brighter nebulas and galaxies, in NASA's list, and it lets the eye see what it cannot detect on its own.
A chair and the moon
The Park Service's advice for a roadside pullout is to set up chairs and watch the sky overhead, and it says a lightweight folding chair keeps each person comfortable and reduces strain. Where the moon is on the night decides how much faint sky there is to see, which is what the moon calendar and the forecast's moon column are for. The Park Service's page adds that on moonless nights the Andromeda galaxy is visible to the naked eye as a fuzzy patch.
What a dark sky is, and is not
NASA's own line is that of the couple of hundred billion stars in the galaxy, the eye sees a few thousand of the nearer ones. What that looks like against the figure people arrive expecting is on the dark skies page. This site publishes no darkness rating for any place, because none of these skies has been measured, and each place's page says so in its own line.