In part 1, I covered three important variables to watch for when choosing a binocular: magnification, aperture and the size of the exit pupil. Now, I'll go through a few more.
Gathering light is important, but not losing it after it's gathered is just as important. Every time light crosses from air into glass or vice-versa, not all light actually gets through: some of it is reflected or scattered away. The loss of light can be of up to 5% on each transition, and a binocular may have as many as 16 air-to-glass or glass-to-air transitions inside it. This could cause as much as 55% of the light to be lost before it reaches your eyes. And that's why lenses and prisms need to be coated.
The function of the coatings is to prevent light from being reflected. High-quality, multi-layer coatings can reduce the reflections to 0.25% of the incoming light, or even less; this will significantly improve the quality and brightness of the image. You want binoculars that are described as "fully multi-coated", that is, all glass surfaces are coated with multiple layers. "Fully coated" means that all surfaces are coated, but not all (or any) have multiple layers, while "multicoated" means that some surfaces have multiple layers, but some have nothing.
A quick way to check for coatings if you have the binoculars in your hands: look at the reflections from the ceiling lights on the objectives. You should see several faint reflections, but none of them should be white. White reflections indicate the presence of non-coated surfaces somewhere in the optics; avoid instruments with this. Also, avoid "ruby coated" binoculars; the reflect large amounts of light and distort the colour of the light that does get through (the image will look greenish).
In short, you need binoculars that allow you to adjust the focus differently for each eye; this can take the form of individual adjustment selectors for each eyepiece or a single central focusing selector with a separate adjustment knob for the right eyepiece. Either of these is acceptable, and mostly a matter of preference (but make sure that you can adjust for eye differences; this is important). Binoculars with individual adjustments for each side tend to be more resistant to water infiltration, but that will depend mostly on the quality of the instrument.
Field of view
This is the amount of sky you can see through your binoculars at a time. For astronomy, the wider, the better, up to a point: if the field of view is too large, you will get distortion near the edges of the image.
The field of view can be expressed in degrees or in "feet at 1,000 yards" (which refers to the width of the image you see). In metric countries, sometimes you also see "meters at 1,000 meters". You want something in the range of 5 to 10 degrees, which is the same as 260 to 520 feet at 1,000 yards, or 90 to 180 meters at 1,000 meters.
This measure is strongly related to magnification; the larger the magnification, the smaller the field of view.
If you wear eyeglasses
Some binocular features are interesting for people with eyeglasses; one of them is called "long eye relief". Eye relief is the distance from the eyepieces at which the image is in focus; that is, it tells you how far away you can be from the binocular while still being able to see the image. For eyeglass wearers who intend to use the binoculars without taking their glasses off, this needs to be long, in the vicinity of 20mm.
Also, ensure that the instrument has retractable or fold-down eye cups, so that you can get the eyeglasses close to the eyepiece without the cups getting in the way.
That said, I personally prefer to take the glasses off and use the binocular with the eye cups up. It is more comfortable for me, and it makes it easier to keep the image forming in the right place (with the glasses on I found it too easy to move my pupils out of the image). Unless you are very near- of far-sighted, you will see everything in focus with or without glasses.
To sum things up, you will want binoculars with:
- magnification not lower than 8x and not much higher than 10x (and definitely not higher than 12x if you don't want to use tripods)
- aperture not smaller than 40mm and not much larger than 50mm
- exit pupil between 5 and 7mm
- fully multi-coated optics
- independent focus adjustment (either one control per eyepiece, or a central one with an extra adjustment for the right pupil)
- field of view of 5 to 10 degrees
- and, if you wear eyeglasses, long eye relief and retractable eye cups
And, finally, you want to test the binoculars before you buy them. Hold it in your hands, make sure that it is solidly built, make sure that it is not too heavy to hold for long periods of time and so on. Repeat this with several models, see how they feel in your hands, see if you can perceive differences in the images. Prices can vary a lot; try to test both cheap and expensive models. Give preference to stores that cater to amateur astronomers instead of retail camera or general stores (that is, do not buy binoculars from Walmart unless you know what you're doing). Also, read this page and do everything it tells you to. Good luck, and clear skies!
(for the record, I bought an 11x56 binocular from Aquila Optical, in Sydney, and I'm quite satisfied with it)