During a brief foray into the realms of astrophotography last night, taking loads of time-lapse photos from random areas of sky, I came across this image showing dozens of Geminid meteors (I stopped counting at 20). The image I took of the same piece of sky later, revealed nothing but stars, which may have had something to do with me altering the settings on the camera. The meteors were not noticeable by naked eye as they were so short lived. It was only after zooming in on my computer that I noticed them.
This was taken with a Nikon 5200D on a tripod - Manual settings: Aperture f8, 10 seconds at ISO 2500.
Not being an expert at this technique I can still give a few tips:
You don't need to use an expensive camera to try this but you do need a tripod and a camera that has the option of manually changing the shutter speed and a manual focus option (automatic focus won't work as it will be too dark to function correctly). Ideally your camera will allow you to change the ISO (light sensitivity) on manual operation. You will also need to use either a remote shutter control or a built-in time delay to prevent camera shake.
It's a bit of trial and error as the higher the sensistivity (ISO) the more light you let in which can result in lots of 'noise' on the image but will also allow faster shutter speeds which will dampen down too much star movement. It depends on what you're after as star trails can look really good as well but on the above image the trails could have masked some of the meteor streaks.
Even a slightly cloudy evening can bring some reward as dim light from nearby towns can transform the clouds into a wispsy frame with neighbours lights painting the trees and bushes.
My goal is to capture the International Space Station streaking through a sky similar to this one. If I achieve it I'll post it and let you know how I did it.