The equipment needed to photograph the constellations is surprisingly minimal, but there some key pieces that will make your photography really stand out.
The first, and most obvious, thing that you need is a camera. Although any camera that is able to take long exposures (~30 seconds) is acceptable, a DSLR is preferred.
The next thing that is near essential is a sturdy tripod. Since we are going to be taking long exposures of 30 seconds or more, we really don't want our camera moving at all.
One thing that is not mandatory, but can make your life much easier when learning how to take pictures of constellations, is a cable release for your camera. Although most DSLR's are capable of taking 30 second exposures natively, there are times where you may want to keep the shutter open longer. For this you either need a cable release or a remote control of some sort.
The lenses used in constellation photography vary with the desired effect. Wide angle lenses are good for including large constellations and foreground objects, whereas longer lenses can get smaller portions of constellations or small groupings of stars. Essentially, whatever you have now can probably already be used, just have fun experimenting!
Finally, a dark sky and a basic knowledge of the night sky is always a plus side to getting constellation images which really stand out. Although many constellations such as Orion and the Big Dipper can be seen over some city lights, it is always best to get to a dark an area as possible. Take a look at www.heavens-above.com to get precise sky charts for your area and time so that you know what constellations are visible when you are shooting!