Taking star trails is one of the easiest forms of nighttime photography. it requires less equipment than full out astrophotography, only a camera that can take a long exposure and a tripod. In a pinch you can do without the tripod.
In star trail photography a long exposure is used to reveal the scene. With illumination provided by starlight the needed exposure will be minutes long, during which time the rotation of the Earth will cause the stars to trail. Each star will trace a short streak on the camera detector as it moves through the field of view.
For a number of reasons taking one very long exposure is a problem with digital cameras. Without getting into a technical discussion of noise, dark current and hot pixels we will simply advise taking short exposures. You can always try a twenty minute or half hour exposure and see for yourself. Thus the technique is to take a series of short exposures, usually one to five minutes long, and add these together in processing. By taking a series of short exposures, the final exposure length is limited only by the camera battery or the arrival of dawn.
If the camera is sensitive enough, and you have a fast lens, you might try starscape photography, where the stars are not trailed by the motion of the Earth. In contrast, star trail photography can be done by almost any camera that can take a long exposure. The difference is in the length of the exposures, long versus short, star trail or starscape.