What do amateur astronomers do, anyway? Help professional astronomers?
Amateur astronomers, for the most part, have roughly the same relationship to professional astronomers that birdwatchers have to ornithologists. There are some amateurs for which one would be hard-pressed to tell the difference. However, for the most part, the two spheres of interest are mutually exclusive. Professional astronomers do science; amateurs look at stuff. Some amateurs help the pros in little ways, but most do not.
What do amateurs look at? After a few planets, the moon, and the occasional comet, what is there to see? I'd think you would become bored.
Amateur astronomers resemble birders in more ways than one. Birders have their "life lists" of species seen that they extend through persistence and travel. Viewable species are cataloged in bird books. Astronomers have compiled lists of potential targets. One such list, the New General Catalog, has over 7000 non-stellar astronomical objects, mostly galaxies, but many nebulas and clusters are also listed. Others enjoy double stars, astrophotography, telescope making, and any one of several dozen sub-specialties.
Can you give specific examples of specialties?
Supernova searching: Some amateurs visually inspect or photograph the 250 or so closest galaxies looking for supernovas. A star lights up briefly where no foreground star appeared before.
Comet hunting: Some people look for comets in the hope of detecting a big one that might make them famous. This work is so hard and dreary that there are only a few dozen people in the world willing to do it at any one time. Both Mr. Bopp and Mr. Hale were amateurs at the time they made their discovery.
Solar astronomy: doing daily sunspot counts or monitoring the sun through special filters.
Variable stars: Making observations of and plotting the light curves of variable stars is the avocation of some amateurs.
Carefully inspecting the planets and moon: Although photography can do a better job of record-keeping than hand drawings or verbal descriptions, something sudden may happen and you may be the first to see it. The professionals would waste resources to be looking all of the time.
These sound as if they require dedication.
As I mentioned before, most amateurs just look at things. A way of spending an enjoyable evening is to sweep out every cluster, nebula, or galaxy brighter than a certain value within a given constellation.
What are nebulas and clusters?
Gas clouds and groupings of stars. In other words, things that have a shape. That's nearly the entire aim of amateurs, to see everything with a distinctive shape. Even variable star observers are concerned with the shape of the light curve. Few amateurs spend much time looking at single, constant-brightness stars. That would be boring.