Linoleum is a common material used in block printing. Designs are carved into the linoleum's surface, which is then coated in ink and pressed onto paper or another material to create a relief print. In a relief print, the parts of the block that are carved away---and therefore aren't exposed to the ink---are not printed.
Linoleum Pros and Cons
Because linoleum is so soft and pliable, it's easier to cut and inscribe images into it, even with lower quality or dull tools. Since less force is necessary for carving, it's easier to make shallow cuts and details. Unlike wood, linoleum has no grain, so you can cut lines or curves in all directions with equal ease. It's also cheap, which can be a big advantage for prolific printers.
However, linoleum's flexibility also makes it more fragile. A linoleum block may not last for as many prints as you might want and doesn't hold up well for large pieces. Because it's so unstable, larger carved-out areas may buckle during printing, and ink distribution can be uneven without a printing press.
If linoleum is giving you trouble, try woodblock printing. Even though wood is a harder, denser material than linoleum, you can use many of the same tools to carve it, as long as they are well made and sharp. Be sure to have good V-shaped, U-shaped and straightedge tools in a variety of sizes on hand, as well as other helpful items such as ice picks, craft knives and chisels.
Choose a piece of a soft wood like pine---cut with the grain, not against it---for your woodblock. Draw your design on the side you plan to print with a pencil; wood lends itself to bold designs, but fine lines and details are possible with the proper cutting tools.
Begin carving, making sure to cut far enough into the wood that the indented surfaces won't fill with ink or touch the paper. Cut away from your body and free hand, taking special care when carving against the wood's grain.
When the design is completed, coat the woodblock with a thin layer of ink with an ink roller. With the block face up, place your paper over the ink and run it slowly through a printing press. If you can't access a press, use a rolling pin or wooden spoon to ensure that the paper makes solid contact with the block's entire surface.
If you're looking to move away from block and relief printing altogether, consider one of the many other printing methods. Monotype doesn't require any carving and doesn't produce a re-printable plate. Instead, you paint an image on a flat, smooth surface like plexiglass and then print it to create a one-of-a-kind image.
For more adventurous printmakers, intaglio is another excellent alternative. Unlike wood or linoleum blocks, intaglio plates only print the recessed areas. One common intaglio method is etching, which involves scraping the desired "black" lines into the acid-resistant coating on a metal plate. Any exposed metal corrodes in an acid bath, creating a recessed design. Before printing, ink is forced into the indented lines and wiped away from the rest of the plate.