The shot below of the Milky Way from the Southern Hemisphere was taken with relatively normal equipment: a Canon EOS 400D / Rebel XTi with the Canon EF-S 17-55mm lens. The camera was set to Manual mode with a 30 second exposure, f2.8 aperture and 1600 ISO sensitivity. The camera was mounted on a tripod, the lens manually focused to infinity and the shutter fired using the self-timer.

Here’s more detail on the kind of settings you should try out for similar shots.
1: Manually focus your lens to infinity, and check that star images are pin points by playing back and zooming in afterwards.
2: Open your aperture. Astrophotography is normally about gathering as much light as possible, so set your aperture wide open using the smallest f-number. That said, many lenses perform better when slightly closed, so if the object is sufficiently bright, you may wish to experiment by slightly closing the aperture - for example, an f1.8 lens may produce sharper, more pin-pointed star images when closed to, say, even just f2.0. It'll also be slightly more forgiving on your focusing. But the downside is less light gathered.
3: Use long exposures. Again, to gather plenty of light, manually set your shutter speed to several seconds. There are a few things to watch out for though. Due to the rotation of The Earth, the stars appear to move across the sky and will leave a trail on long exposure photos. The effect can be quite attractive, but to avoid it, either keep exposures sufficiently short, or if you're really into astrophotography, use a special motorised mounting which follows their motion, thereby effectively keeping them still.
Assuming you're shooting from a fixed tripod though, I generally find you can avoid star trails by keeping exposures under 20 seconds when using an effective focal length of 50mm. At 25mm, you could therefore do 40 seconds, and at 100mm, 10 seconds. As you take pictures further from the pole though, the trailing effect is greater, so you’ll need shorter exposures to avoid it.
Obviously exposures of this length require a steady tripod and either the self-timer or a cable release to take the shot without wobbling the camera.
4: Increase the ISO. Another way to maximise the light entering the camera is of course to increase the ISO, although this will in turn increase undesirable noise levels. If you want to keep exposure times short though or capture particularly faint objects, higher ISOs are normally necessary.
5: Set your white balance to daylight, as Auto settings can produce unfaithful colours.
6: Experiment! Try a variety of exposure times, focal lengths and ISO settings to see what produces the best results for the object you’re shooting under the conditions of the day (or evening!). Unless you live (or are photographing) miles away from civilisation, you will have to deal with light pollution from street lamps which will turn your sky orange or green. If this is plaguing your photos, you may have to reduce the exposure time or ISO setting to retain a dark-looking sky.
Have fun!
Gordon Laing