If you have Digital SLR, you can take some beautiful wide-field images with just the camera on a tripod. This is where I would suggest you start if you are just getting into astrophotography with a DSLR.
Next, you may want to shoot some images with your camera and lens mounted piggyback on your telescope. You will need an equatorially mounted telescope (not an altazimuth mount) to take pictures longer than about 30 seconds.
Once you've got some experience, you may want to hook your DSLR up to shoot through your telescope. In this case, the scope takes the place of the camera lens. You will need some accessories to use it like this to shoot astrophotos. At a minimum, you will need a T-mount and adapter.
If your telescope has a 2 inch focuser, you will need a T-Mount ($20) and 2-inch Adapter ($30). The T-mount has a bayonet flange that mounts to your specific type of camera, such as Nikon or Canon. The 2-inch adapter screws into the T-mount. The 2-inch adapter then goes into the 2-inch focuser on your telescope.
Not every telescope has a 2-inch focuser. A 1.25 inch focuser and adapter will probably vignette on a DSLR.
The T-mount and adapter are all you really need to get started shooting through your telescope. You can simply use the camera's self timer to open the shutter for exposures up to 30 seconds. This will work much better than trying to press the shutter button with your finger as this will probably move the telescope and blur the picture.
For exposures longer than 30 seconds, you need to set the camera to the "bulb" setting, usually the next shutter speed that comes up on the camera after 30 seconds. The bulb setting holds the shutter open as long as you hold down the shutter release. This can be a serious problem because there is no way you can do this with your finger and not move the telescope during a long exposure. So you will need some type of remote release such as a wired remote. These usually plug into the side of the camera.
Some cameras, such as Canon's Digital Rebel series (300D, 350D, 400D) use a simple mini stereo plug for the bulb release. You can even make one of these yourself very inexpensively. Some Nikon cameras use an infra-red remote release. Most advanced amateur and professional digital cameras, such as Canon's 1D, 20D and 30D, and use a proprietary N3 plug. You will have to purchase a cable from the camera manufacturer for this type of plug.
Once you have the correct kind of bulb-exposure cable, you can start taking long-exposure astrophotos.