Newbie question on atsrophotography

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What effect does exposure time have on images?

Say I just wanted to take a picture of some stars in the night sky, just with a cammera, no other optics...

Is it the exposure time that will show the stars?
 
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The exposure depends on the sensitivity of the film (ISO setting) and the focal length of the lens. The longer the exposure the more stars will be visible, but if it is longer than around a minute the stars will be blurred into lines as the Earth rotates.
The easiest way is to try different settings and see.

It's a little more difficult with a digital camera.
 
Open the aperture all the way, focus at infinity, and take exposures of several seconds up to a few minutes, depending upon your subject. Beyond that you'll need some kind of clock drive, unless you desire star trails in your images.

- Warren