Determine the size of the linoleum you want to use. You can purchase it in the desired size or in a large sheet that can then be cut to size. Place the sheet of linoleum on the bench hook. This will hold the surface firmly so you can cut the linoleum accurately and safely. Lay out the linoleum cutter as well as the interchangeable attachments.
Draw an outline of the picture on the linoleum, using a pencil. Hold one arm across the linoleum to stabilize it, then begin cutting the surface with the other hand. Cutter sizes vary: a narrow (liner) cutter is best used for high relief, a wide, U groove and V groove should also be used to achieve a variety of effects. For optimum results, use varied cutters, much like a painter would use different brushes; this will determine the shape and size of the painting.
Remove all stray pieces of linoleum for a smooth, clean surface. Decide on the color(s) for your painting and place the acrylic paints in a palette. Add water to make a watercolor like consistency, creating a stain. Linoleum is absorbent, so the water and acrylic paint mixture works well.
Begin painting the deep, carved grooves with darker colors. This will give the painting shadow-like effects. Lighter colors can be used on the flat surface for contrast. Remove paint that has spilled into any unwanted areas with paper towel. The acrylic paint is water-resistant, so it is optional as to whether you use a sealer. A spray fixative can be used, and the finished relief painting can then be framed.