Here's a shot I took last september on a moonless night at the Great Lakes Star Gaze in Michigan. This is a good (although not excellent) dark sky site.
Milky Way by
Tim Campbell1, on Flickr
The EXIF data is intact if you want to look at it, but I took this with a Canon 5D II (full-frame camera) using a 14mm f/2.8 lens.
The shot was is a 40 second exposure at ISO 1600 at f/2.8. The lens was manually focused (auto-focus switch was turned off.)
BUT... this shot is processed. The straight-out-of-the camera shot was fairly muddy. Guys who have been doing this a lot longer than me could probably make this look a lot richer. There was more background skyglow than I wanted, but to get a TRUELY dark sky site would require quite an expedition (there are some locations in northern Michigan with amazing dark skies.)
You want to get the exposure times reasonably short, so don't use f/20.
Use your widest angle. f/2.8 is 5 & 2/3rds stops faster. That means it'll require about 1/50th of the exposure time. The problem with long exposures is you'll need a mount which tracks the stars and is aligned to Earth's polar axis otherwise you're going to get star trails. When I took my shot it was on a normal tripod (with a ballhead). This shot was not "tracking" the stars (even though I do have a camera mount which allows me to piggy-back the camera onto one of my telescopes.) At 14mm and a 40 second exposure I knew I wasn't going to get star trails... yet.
If you've got an 18-55mm kit lens then you could use 18mm & f/3.5. At ISO 1600 you'd need about a 1 minute exposure and can tweak from there. If you go to f/4 then you'd need to increase the exposure to about 1m20secs. And of course if you use ISO 800 for less "noise" then you'd need to double the exposure times, but at some point you'll start noticing elongated stars (starting to grow tails) from the movement of the sky during the long exposure.
The stars straight out above Earth's equator (declination 0) are moving at a speed of 15 arc-seconds per second of real time (that's not exact because the Earth spins 360º in only about 23 hours and 56 minutes... not 24 hours.) Every 4 seconds they move 1 arc-minute. In 4 minutes they move 1 degree (unless I screwed up my math, but I think that's right.) To help you imagine just how fast that is... the full moon is about 30 arc-minutes (yes, just 1/2 of a degree) from edge to edge. That means the moon will have moved in the sky by it's own width in just about 2 minutes! The stars nearer to the poles don't appear to moving as fast (Polaris, for example, hardly seems to move at all even though it's technically about 40 arc-seconds away from the true celestial pole (yes... if you could slide the moon up to the pole, you could fit the moon between Polaris and the true celestial north pole and still have a tiny bit of room to spare.)
Update: Ok, apparently Flickr captures the EXIF and makes it available on their site, but strips it from the image imbedded here (the image I uploaded to Flickr had the EXIF in it.) You can view the EXIF by viewing it at Flick are picking "Actions" -> "View EXIF info".