Binoculars are the most underrated astronomical instrument, and the reason is that they do the two things a telescope does worst: they show large objects whole, and they need no setup at all so they actually get used.
What to look at first
The moon along the terminator, where craters catch the light. Jupiter and its four bright moons, visible as points beside the planet. The Pleiades, which fill a binocular field and look far better than in any telescope. The double cluster in Perseus, the Andromeda galaxy as a clear oval, and the star clouds of the Milky Way through Cygnus and Sagittarius.
How to see more with the same pair
Brace against a wall, a fence or a car roof, or lie back in a reclining chair, which removes shake and the neck ache at once. Give your eyes twenty minutes to dark adapt and avoid white light after that. Use averted vision on faint objects, looking slightly to one side, which is where the retina is most sensitive.
Mounting them, which doubles what you see
A tripod adapter costs very little and the improvement is immediate and large. Detail that was smeared by your pulse becomes visible, and faint objects appear that were previously below the threshold. Almost every experienced binocular observer mounts them for serious looking and handholds them for sweeping.
What sizes suit
Ten by fifty is the standard because it delivers a five millimetre exit pupil at the edge of handheld steadiness. Seven by fifty gives a wider brighter view for younger eyes. Fifteen by seventy and larger show substantially more and require a mount, which is a fair trade if you have somewhere to set one up.
Questions people ask about binoculars
Can you do astronomy with binoculars?
Yes, and a great deal of it. Clusters, the Milky Way, the brighter galaxies and nebulae, comets and the moon are all binocular objects.
What can you see with 10x50 binoculars?
Dozens of Messier objects, the moons of Jupiter, lunar detail, the Andromeda galaxy, and the Milky Way resolving into stars from a dark site.
How do I see fainter objects in binoculars?
Dark adapt for twenty minutes, brace or mount the binoculars, and use averted vision by looking slightly to one side of the target.