The most popular print processes available are:
Giclee prints are premier quality. These are made using an inkjet printer and archival quality inks. The paper is usually chlorine-free, 100% cotton rag. The artist will often collaborate with a master printer to scan in the work and get the colors just right. Because all of the materials are long lasting and the end result is a near perfect reproduction, giclees are highly sought after. But be warned: this term is not standardized.
Serigraph prints are another high quality process. An artwork will be scanned, and the printer will make a silk screen for every single color, with each screen being applied in layers. This can be an arduous process. If the artist wants to use oil paints, the printer may have to wait two days between layers. When you consider that some prints can have hundreds of colors, you can see how serigraphs take a lot of patience.
Lithograph prints are usually made using four colors in a rapid process. The printer creates a metal plate for each color and applies these in layers. The production is much simpler, but the quality and value can suffer.
Canvas prints are inkjet prints made directly to a canvas that can be stretched over a frame. This allows the work to appear more like a painting.