Binoculars for astronomy work should have an aperture of at least 50mm but it must be said binoculars over 50mm do tend to be much more expensive and heavy so 50mm is good. A magnification of 7x or 8x is the best but a 10x can be used. The 10x may be difficult to hold steady but if supported on a wall or fence can be used. So look for a 7 x 50 or 8 x 50. What about cost? Normally the old adage ‘you get what you pay for' is true. About £50 will normally buy a good pair but spend as much as you can afford.
Getting the best out of binoculars is dependant on them being adjusted to suit your eyes and this is easily done. First look at the eyepieces, one will be adjustable the other will be fixed. To carry out the adjustment take the binoculars out on a clear night and select a bright star. Aim at the star and close the eye which is looking through the non-adjustable eyepiece. Using the central focuser bring the star into focus so that it appears as its smallest point. Change eyes and adjust the eyepiece by turning the eyepiece adjuster until the star appears as its smallest point. Now open both eyes and the stars should be small and sharp. Some cheaper binoculars may display a flare or spikes around the stars but this is not a big problem if the effect is not too noticeable. The nature of stars themselves will not be able to be studied using binoculars only the positions and patterns so some distortion of the images can be acceptable. In fairness it must be said that binoculars will not show a lot of detail on the Moon or the four brightest planets. The four largest moons of Jupiter should be visible and the rings of Saturn might just be glimpsed in the best quality 10 x 50 instruments. It may be found useful to rest your elbows on a wall, fence or even use a broom (bristle end up). This is particularly useful if you are using a 10x or more pair of binoculars to avoid wobble. It may even be useful when trying to make out detail even with lower power instruments.
Now a brief word on how to use the binoculars. It is good fun just to sweep through the sky and see what there is to find. As the sky is swept, pairs of stars can be seen and even what appears to be groups of stars. These pairs and groups may be associated with each other or may just be in the same line of sight but are still beautiful to see. Having had a random look around the sky to become familiar with using the binoculars, a more scientific approach can be taken. By using a star chart or monthly maps of the sky or even the ‘What's Up' notes on this site, interesting objects can be found. Some of the brighter Messier objects can be seen using binoculars. The Globular Cluster M13 in Hercules can be seen as a patch of fuzzy light as can the Great Spiral Galaxy M31 in Andromeda. M45 the Open Star Cluster in Taurus, known as The Seven Sisters, is seen at its best in binoculars. All the stars of this cluster are within the field of view of binoculars but cannot all be seen in a telescope which has a much narrower field of view.
The Moon is a magnificent target for binoculars. It is large bright and has a lot of detail to study. As the Moon progresses through its phases from a thin crescent to full, different areas become more favorable to observe. The ‘Terminator' (the dividing line, between the Sun lit side and dark side) gives the highest relief due to the long shadows cast by mountains and craters. As the terminator moves across the face of the Moon different craters on the terminator become much clearer to see. A very interesting thing to do is to sketch the craters as they are seen and then compare the sketch to a map of the Moon to identify the craters.