Ad compositors put together the advertisements you see in the newspaper. Sometimes they design the ads themselves based on a client's needs (which can change at the drop of a hat), but often they replicate or scan in a client's existing design. They will also do a lot of typesetting, proofreading, and correction. Ad compositors generally don't need to know how to draw or do illustrations, but if they do have artistic talents, they may find themselves called upon to do more interesting stuff if they work in a good shop (or, alternately, they may find themselves frustrated that they're never called upon to use the full range of their skills).
These days, most ad compositors do their work on computers (often Macs) using programs such as Multi-Ad Creator, Photoshop and Pagemaker. However, some compositors may do physical paste-up with waxed bits of printed stock art, text segments and design elements cut up with an X-acto knife and assembled on galley paper over a light box.
My year working part-time as an advertising compositor was the most stressful job I've ever had, and at minimum wage, no less. Our ad room had deadlines three times a day; the workload and pressure were incredible. A friend of mine worked professionally as an ad compositor for a small daily paper -- she was unbelievably burnt out after a year, and I think she maybe got $18K a year in exchange for elevated blood pressure and perpetual sleep deprivation.
If you seek out a job as an entry-level ad compositor, you can expect to learn a lot about graphic design and computers in a short period of time. Most newspapers, if they don't actually require a portfolio of advertising design work, will require at least some journalism or graphic design coursework and evidence of computer proficiency before they'll hire you. You may also have to pass a typing test or test on keyboard shortcut commands (I had to take the latter; I don't know how common that is, though).