Star trail images show the motion of the stars over a long period of time, making beautiful arcs. Back in the film ages the method for making these images was to open the shutter and let it go for hours, but that method doesn't work too well with digital cameras. When the shutter is left open for a long time on digital cameras all kinds of thermal noise, exposure issues, etc. can arise. The best method with digital is the take a series of short (~20-30 seconds) exposures then stack them in specialized software to make the arcs.
This method is also the general idea behind the creation of astro time lapses. Instead of stacking the images one atop each other, as seen in the making of star trails, the images are displayed one after another to make a movie of the stars moving. Below is an example:
My preferred software for making star trails and time lapses is the free Startrails application - http://www.startrails.de/html/software.html. I find this program to be the most user friendly and easiest way of making high quality star trails / time lapses. It will be this application that I will use in this tutorial.
Most of the techniques apply to both projects (setup, composition, technical details), and I will cover those first. After those I will address some of the nuances to be aware of for each project.