You need a camera which is completely mechanical. A modern electronic camera will drain its little battery in short order. I used an old Canon TX body.
Film does funny things during a very long exposure. A high contrast film like Velvia makes the trails stand out more than a lower contrast film like Sensia. Background light causes the sky to turn a dark olive green color.
Use a wide angle lens. A 35mm lens will barely cover the area from the horizon up to Polaris, giving you just the bottom half of the arcs. This angle is the same as your latitude. I used a 24mm lens for this picture. The choice of f-stop is somewhat experimental -- f/5.6 to f/8 seems to work well without letting the background get too bright.
You need to find a very dark place for this, far away from city lights. High elevation is good too, because there is less air to diffuse the starlight. The phase of the moon is paramount. You can only do star photos for a few days around the New Moon period. Summer is not good because the nights are so short. September is good because the nights are longer and the skies are generally clear.
If you want a photo with the arcs around a central point, you have to aim the camera to the north. Obviously you have to use a tripod. You might include some terrestrial object in the foreground, which will become a silhouette. Wait at least two hours after sunset to open the shutter. Put the camera on "B" and use a locking cable release to hold the shutter open. Then you have to wait around all night so you can close it two hours before sunrise. This is the worst part of this whole endeavor. To avoid this inconvenience, I built a timer gadget from two alarm clocks and a small motor that pushes on a cable release. I also built a foot-tall wooden tripod for this purpose, rather than use my good tripod.
So what can go wrong? Plenty. Just one cloud drifting over will cause gaps in the star trails. Airplanes leave straight line streaks and their strobe lights leave dotted lines. About 80% of the photos will have one of these two problems. If the air is humid, dew might form on your lens. Then there are things you never consider -- one night my little tripod was knocked over by some animal.
So you go to all this trouble, and you get one frame. One measly frame. And it is probably messed up by a cloud or an airplane. With conventional photography you can easily use up several rolls of film in a day and probably get something good, but with stars you go through all this hassle and get just one frame. It can be very frustrating. That just makes it all the more satisfying when you finally achieve the perfect shot.