The SLR camera should be as manual as possible and have one important feature: a B setting for "bulb" (time exposure).  Stars appear as faint objects and to overcome this, you need to keep the shutter open for about 20 seconds (on average). Any manual SLR camera will work (Olympus, Nikon, Canon, etc.).  I use a Minolta and a Pentax P30n.  A very popular one is the Pentax K1000.  Unfortunately, stores sell mostly automatic cameras which have no bulb setting and use batteries (the latter is bad because the batteries shut down in the cold).  But some stores are selling used manual cameras and the online auction house Ebay is a very good and reliable source.

 

Since the exposure lasts about 20 seconds, the camera needs to be stable, thus the need for a tripod.

 

Since pressing down the button would make the camera vibrate, a cable release is used.  It screws into the camera (all manual SLR cameras have such a screwhole), you push it, it opens the shutter, you tighten it and then the cable release keeps the shutter open (without making the camera vibrate) until you release it.  The photo on the left shows how I lock the cable release.

An SLR camera may look rather complicated.  But for astrophotography there are three easy settings: (1) the B setting (bulb, time exposure) as mentioned before, (2) leave the shutter wide open, i.e. choose the smallest number on that scale (1.4, 1.7, 2.0, whichever is the smallest), and (3) since stars are very far, focus at infinityµ.
 

...  The normal 50 mm lens that comes with all SLR cameras is ideal.  Sometimes I use a 28 mm wide angle, rarely a 200 mm zoom.  The maximum exposure time depends on the focal length: if you expose for too long, stars start "moving" (star trails due to our Earth's rotation).  A zoom lens for example takes a picture of a fairly small area and therefore the star trails will appear after only a few seconds.

...

As a rule of thumb, divide 1000 by the focal length: for the wide angle 1000 / 28 = about 40 seconds; for the normal lens 1000 / 50 = 20 seconds; for the zoom 1000 / 200 = 5 seconds.

You notice the disadvantage of the zoom lens right away: at 5 seconds (no star trails), you get very little light and thus faint stars or even an underexposed picture (making the sky background an ugly brown).
 
 
 

Let's discuss the exposure times for the 50 mm lens: the maximum time before star trails is roughly 20 seconds.  Make a shot  for 100 seconds and you will definitily get star trails.  Now, the closer the stars are to the North Star (Polaris), the longer you may actually expose.  That's because the stars near Polaris are "moving" less.  A picture of the Little Dipper can last about 60 seconds without having star trails.
 

Film has different "speeds".  Here you see ASA 100, 400, 800.  In photography, we have to make a compromise when we use one film or the other.  The slower the speed (smaller number), the smaller the grains on the emulsion, meaning very sharp images.  That's why most films are ASA 100 and 200.  But they need a lot of light, thus you need to be outdoors during a sunny day or use a flash.  For astrophotography, we need fast films (large number).  (Indoor sports photographers use fast films as well because of less light [despite lamps and flash].)  Fast film means that they get an image with less light, thus shorter exposure times are possible for faster action.  However, they are grainier, meaning that they are not as sharp.  Nevertheless, their quality is certainly good enough for what we want to do.  I used ASA 1000 when I started, but now routinely use ASA 400.

I recommend starting with rolls of 12 images.  That way, you know very quickly if you do it right and what you like to improve (don't feel foolish when you get bad photos; professional photographers readily admit that they did every mistake that possibly could be made).  As with any kind of photography, expect to use lots of film and expect that among the many pictures, you will have a few that you really like.
 

Usually you want to expose to the maximum since you want to gather as much light as possible.

PHOTOS
 

Here are exceptions:

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The Scorpion on the left was shot by accident (the cable release wasn't locked correctly, so the shutter closed after 2 seconds).  However, that way only the brightest stars appeared, outlining the familiar form of this constellation.  The Scorpion is a perfect example since it's prime stars are rather bright.

This picture is of Cassiopeia.  It's in the form of a W (tilt your head a little to the left, then look just right of the center).  The shot was a typical 40 seconds with a 50 mm lens (since it's close to Polaris, exposure time can be longer than the typically recommended 20 seconds).  It's a pretty picture.  It has one drawback if you just want to see the W: due to Milky Way running right through Cassiopeia, too many stars appear.  If you just want the W without the Milky Way, expose for about 10 seconds.
 
 
 
 
 
 

PICTURE OF STAR TRAILS.

Once in a while you want to take star trails.  Depending on how long the trails should be, expose anywhere between 2 minutes and a couple of hours.

PICTURE OF FLASHING AIRPLANE.

Taking a picture of an airplane flashing through a constellation adds to appeal.  You could also catch a satellite on film.

When photographing the aurora I use a 28 mm lens to cover more area in the sky.  The maximum exposure time without star trails would be 40 seconds, but it's photographing towards North, thus the exposure time lengthens to about 60 to 80 seconds.  And, since I like to get as much detail and color in as possible, I recommmend taking photos anywhere between 1 and 3 minutes (and yes, then you will get star trails).
 

PICTURE OF COMET

Can we use a flash for astrophotography?  Of course not.  A flash is used, so that its light is reflected off an object and then enters the camera lens.  Moon, Sun, planets, stars, etc., are too far to reflect a flash's light.  Plus they either emit their own light (Sun, stars, galaxies) or already reflect light (planets, Moon, comets).

That stars have spokes is actually not true.

As far as observations with the naked eye, binoculars or a telescope are concerned: the human eye is not a perfect optical instrument, so it does spread out the light from a bright star into many spokes.  Especially people with bad eyesight can notice that when they look at bright street lights without their glasses or contacts.

This is what happens on photos:

Both pictures were taken with the HST (showing parts of the Orion Nebula and of the globular cluster M33).  Notice that the bright (over-exposed!) stars exhibit four major diagonal spokes and four fainter ones in between: HST's mirror needs to be mounted and apparently it has four major and four minor stress points/lines due to mounting, and these "warp" the mirror enough so that these stress points show up as star spokes on long exposures.  PS  the purplish stars in the Orion shot also exhibit Airy disks.  These are explained in my Hubble lecture.