Astronomy, as a science, is essentially the description of stars using mathematics.
Astrophysics, as a science, is essentially the descriptions interactions of physical properties of celestial objects.
The amateur is capable of working in this realm by putting their equipment to use and devoting a small amount of time into the effort. In ye olden days, astronomers scanned the heavens first with their eyes (Messier and Hershel) and later with cameras (Arp and others) where foggy patches were 'discovered', cataloged, and classified. These long lists of objects (growing into the millions now) were further scrutinized by scientists and fundamental changes to understanding of the underlying physics of these objects resulted.
Today's observer does little more than revisit the discoveries of old. Discoveries came with advances in equipment and data. Today's astronomical discoveries are coming from databases of data. Some of these databases are vast and essentially undigested. This is the golden opportunity for amateurs to apply themselves both for their own education and gratification, as well as, to bring the interesting objects to the attention of the professional.
Many AL members are observers. They have large, albeit basic instruments, they use to sweep the sky and visit lists of discovered objects. It still takes research to gather an understanding about the astronomy and astrophysics that are involved with these objects. One place to do the research is the Internet, and a few particular places give non-science observers raw images of objects as well as a basic understanding together with questions that scientists are tackling and an email address or phone number.
Hanny Van Arkel is a schoolteacher living in the Netherlands that made a discovery in this emerging neo-classical sense. We used her computer as a telescope, patiently scanned images in these vast expanses of data-space, and brought this object to the attention of the pros. Her object: a gaseous object very near IC2497. An in-depth discussion is at: http://www.sciencedaily.com/releases/2008/08/080805124001.htm You can try your hand at: http://www.galaxyzoo.org/
Let us know what you discover!