Binoculars are essentially two small refracting telescopes put together and are very cheap, but can be great for looking at the stars, especially when coupled with a tripod to eliminate the shaking that we all have some degree of in our hands. With the shaking eliminated, dimmer objects can be resolved.
When it comes to buying binoculars, they can be picked up at most department and sporting goods stores for under $50. For beginners, any binoculars will do, as long as they met a few basic specifications that are suited to astronomy.
Binoculars are sized by two numbers, 10x50, for example. The 10 refers to the magnification power and the 50 refers to the lens aperture. For astronomy, a pair of binoculars with a magnification of ten or twelve is ideal. Anything less that ten is often underpowered for viewing some brighter deep sky objects, especially if light pollution is an issue. Anything much greater than twelve often is a problem because of two factors. First, at higher magnifications, shaking in your hands can really become a problem. Second, the higher the power, the smaller the field of view. Even for experienced astronomers, a generous field of view is desired to eliminate any need to search, which is better spent looking at the sky. With binoculars, searching should not consume much time.
The second number, the aperture, is also important. Anything less than 50mm won’t let enough light in, which will limit what you can see. In astronomy, aperture is everything. For aperture, higher is always better. If you find two pairs of binoculars for close to the same price, say a 10x50 and a 10x70, go for the one with the larger aperture. With a larger lens, more light is let in and objects will look brighter.
Another important consideration for astronomy binoculars is field of view. For most people, anything less than a 5 degree field will be too small thanks to both the narrow field making things harder to find and for being more prone to hand shake. Personally, anything with a 5-7 degree field is the happy medium. Generally speaking, binoculars with 7-10x power fall into these fields of view.