In any given year, several comets will become visible in small telescopes. The usual telescopic appearance of a 7th-9th magnitude comet is similar to that of an unresolved globular star cluster or a galaxy. This is why Charles Messier, in the 18th century, drew up his catalog of deep-sky objects--to prevent confusion of these with the new comets that he was always hunting. The observational method to distinguish a comet from other diffuse objects in the sky is to watch for motion: a comet's position among the stars will slowly change from night to night. Sometimes this motion can be noticed within an hour's viewing.
Because comets can brighten or fade rapidly, the Web is a good source for up-to-date information. Here are some of the best comet sites.
Some comets, like Halley's, are periodic, with orbits that take less than 200 years to complete. Others have orbital periods of millions of years. The orbits of some periodic comets cross the Earth's orbit. If there is dust strewn along the comet's orbit at the point where we cross it, we get a meteor shower. Meteors offer unique and intriguing observing opportunities.