Start with a good quality scan or digital picture of the art to be printed; practically everything in printing starts digitally. The quality should be as high as possible. No matter what print method you choose, the old standard: "garbage in, garbage out" certainly applies.
Printing at home using your laser or ink jet printer is an option for smaller quantities or when you're just starting out. Selecting the best printer you can afford is the first thing to do; one that uses separate ink tanks for each color will save you money in the long run as well as improve the color quality.
For the adventurous, screen printing may have a substantial setup cost for the raw materials, but does afford the artist free reign as far as quantity and quality are concerned. Best suited for simpler uses of line and color, the individual nature of each print increases its value and can be an art form in and of itself.
The quality of copiers has improved to the point that they can be trusted with most single-color line art and even some color pieces. Make sure to get some test copies before committing to a large quantity and explore the various paper options the shop has available.
Print on demand services, usually contracted over the Internet, are becoming increasingly popular choices for artists with little in the way of start-up funds and no space to keep an inventory, much less time to handle selling and shipping. Your profit margin may not be very high on these sorts of prints because the overhead of the printer will take a large share, but the trade-off comes in the form of a built-in distribution system and the lack of monetary risk to the artist.
Commercial printing shops, either local or overseas, will probably be your most expensive option, but can offer a supreme level of quality. Frequently, you will need to place a minimum order to justify the expense. Your per unit cost will decrease the more you buy, but keep in mind that you will then have to store the prints, so make sure not to overbuy.