Purchase a linoleum block. This is a thin piece of linoleum that is mounted on a wooden block which makes it easier to carve the linoleum. These blocks come in all sizes. A less expensive alternative is to glue a piece of linoleum tile onto a block of wood.
Draw your design on the linoleum. Remember that it will print in the reverse. If you do not want to draw directly on the linoleum, you can draw your design on tracing paper with a soft pencil. Put that side down on the linoleum and trace the lines with a hard pencil to make the lines transfer onto the linoleum.
Cut away the part of the design you do not want to print with a linoleum carving knife.
Squeeze a small amount of linoleum block ink on a piece of glass. With a brayer, spread the ink so that it a covers the brayer in a thin layer. Too much ink makes your lines blurry and not enough ink will cause spots of your linoleum not to print. Roll your brayer over the linoleum until you have full coverage of your design.
Place your block, linoleum side down, on a piece of print maker's paper or card stock that is slightly larger than your block. Apply firm, even pressure on your block to transfer the ink to the paper. Carefully peel the paper off the block. Set your print aside to dry. Clean your brayer and linoleum with soap and water.