Choosing a Camera and Accessories
The first and most important thing you need for astrophotography is a good camera. Look for a camera that can be set to take low light pictures. The camera should have a variable shutter speed so as to be capable of the long exposures typically needed for imaging dim objects in the night sky.
You also need some accessories for your camera. A good, sturdy tripod is a must for any photography with long exposure times. You should also look into filters for your camera, as many astronomical objects appear best through such filters. Keep in mind that the CCD chips in most digital cameras respond most strongly to red light, so objects on the blue end of the spectrum will need longer exposures for the same effect.
Astrophotography without a Telescope
You don't need to run out and buy an expensive telescope for astrophotography. If your camera has a good zoom lens, or can be fitted with one, you can image many of the brighter astronomical objects without a telescope. Images of the moon, for example, do not need much magnification, and you should be able to take such images with a zoom lens and a tripod. Solar photography during the day can also be accomplished without a telescope. Keep in mind that you will need a solar filter in order to take any such photos. Do not look at the sun directly through your camera if you do not have a filter.
Wide views of the sky are popular for astrophotographers without telescopes. Long exposure photos of the stars take excellent images of the stars' movement throughout the night. If you want to image an object and not have the movement trails, you will need a motor attached to your camera in order to follow the object as the Earth's rotation causes it to shift position.
Astrophotography with a Telescope
Most astronomers want to produce images that can only be seen with the high magnification offered by a telescope. Any telescope can be used for excellent astrophotography, as long as the mirrors and lenses are of good quality and can be focused precisely. The one key piece of equipment needed is a motor to move the telescope and to keep your images from rapidly moving out of your field of view. Many telescopes come equipped with tracking motors, or you can buy one separately from a manufacturer such as Celestron, Meade or Orion.
You will need to attach your camera securely to the telescope. To do this, you need an adapter that will attach your camera to a telescope instead of to a lens. Major camera manufacturers like Canon also produce these adapters. Make sure your telescope is pointed correctly before you start imaging. If you have a digital camera, you can see your astrophotography results right away.
Keep in mind that images taken with Earth-based telescopes are necessarily subject to atmospheric distortion and probably will not be as clear as those shots taken by space telescopes. Also remember that the telescope flips images because of the optics. The top of any image will therefore be the South, and the North will be at the bottom. If this is an issue, you can flip the images afterwards on a computer.