It is not easy to take a picture of stars in the big city like Chicago due to heavy light pollution. Whenever I go to some rural areas or vacation places, night sky is very interesting subject for the pictures.
Couple years back, I went to Big Island, Hawaii with my wife and had a chance to join Mauna Kea Star Gazing tour. It was very fun and exciting experience. While others were listening to a tour guide and looking at stars with telescope, I enjoyed taking pictures of stars. Here is some tips to take a star gaze pictures.

First of all, you will need a very sturdy tripod as its exposure time is very long. A remote shutter release is also good to have or we can use in-camera timer to avoid any motion by pressing shutter.

There is a Rule of Thumb for this subject with respect to your camera gear especially related to lens focal length. It is generally to preserve sharp stars in the pictures. Since the sky at night is really dark, your exposure time becomes pretty long, which may cause blurry stars as it rotate around earth (in fact, earth rotates not stars).

– max shutter speed = 600 / focal length

So, for instance if you use 50mm lens, your maximum (slowest) shutter speed is 600 / 50 = 12 seconds.

I figured good start point is for 24mm lens is 30 seconds at iso 2000 or 3200.
From this, just try it out and adjust exposure setting such as aperture and iso.

Here is a picture I took at that time.

[30secs. f/3.2. iso 2000 @ 27mm]

After taking pictures, quite a bit of post-processing is required to boost stars in such dark scene. also need to remove some noise.

Another tip here is to include some context in the picture instead of filling it with only sky.

some useful reference
http://photography.nationalgeographic.com/photography/photo-tips/secrets-milky-way-richardson/#

another reference from web posting
14mm, 30sec, f2.8, iso 8000 (see it here. http://www.flickr.com/photos/benison/7825505822/)

You can find more pictures of my trip to Big Island at my flickr site. Here.