Catching the Light has a lot of information on astrophotography and is a great place to start.

However, with just a dSLR, it can be pretty challenging to do deep space photography, many are using telescope with mount adapters for their cameras and motorized star tracking to keep everything in focus. The last is a big factor, without star tracking, of some sort, you're going to end up with star trails which, admittedly, can look really cool.

As for film versus digital, it probably doesn't really matter. One thing, however, to bear in mind with some digital cameras is something called "dark frame subtraction" (or long exposure noise reduction) which is used to remove sensor noise, usually from heat. Many cameras allow you to turn this off, which you want to do, but some don't, so check your camera model to be sure. In general, it is better not to have that on because it will double the length of time for each exposure and it can usually be handled in post processing with a single dark frame you take yourself. A dark frame is just a long exposure with the lens cap on.

Anyways, the website I linked has a lot more detail and probably explains it better than I am...