How To Take Pictures Of Stars
You can take pictures of stars with just a SLR and a tripod. However, if you want the stars to stay relatively sharp, you are limited to a few seconds exposure. This is because the stars move across the sky, which appear as streaks in relatively long exposures.
If you intentionally want to have streaking stars, then it is a good idea to use the bulb exposure mode. This allows you to make very long exposures for as long as you hold down the shutter button. Having a remote shutter release to trigger the shutter is a good idea for this kind of work, because it will reduce the problem of accidently pushing the camera when holding the shutter button down.
Picture Noise Problems
One problem with long exposures is random noise from the sensor. The heat creates a background noise that adds up over the length of the exposure. If your camera has a dark frame subtraction mode, it can be useful to use that to subtract the noise from the picture. This works by taking an extra photo with the shutter closed to measure the background noise, and then subtracting those pixel values from the image of the stars.