Board and batten siding makes an inexpensive covering for shed walls, since you can use rough-sawn lumber that doesn't need to be kiln dried. The "boards" are 6 to 12 inches wide, nailed vertically. The smaller "battens," 2 to 3 inches wide, cover the gaps between the boards. If you nail the boards so that they have room to expand and contract with humidity, you can minimise splitting. To save money, order boards directly from a small local sawmill or reuse old barn siding.
Nail horizontal furring strips to the outside of the shed's studs. Space them 2 feet apart. Use 2-inch by 4-inch boards for a large shed or 1-inch by 3-inch boards for a small shed.
Measure the height of the shed on one end of a wall with a measuring tape and mark a 1-inch-by-10-inch board that length. Saw the board to length. Align it with the end of the wall and nail it vertically to the furring strips with 3-inch common nails. Put one or two nails into each furring strip near the centre of the board, to allow the board to expand or contract in width.
Nail the rest of the boards the same way, starting beside the first one and working to the other end of the wall. Space them with a gap of 1/4 inch to 1 1/4 inches, selecting the distance so the edge of the last board will line up evenly with the end of the wall. Check every few boards with a level or plumb bob to make sure that they're vertical.
Saw a 1-inch-by-3-inch board the same length as the first board. Nail it at the centre over the gap between the first and second boards, using one nail for each furring strip. Center the nail so that it goes between the wide boards and directly from the batten into the furring strip. This allows the wide boards to expand and contract without splitting the batten.
Nail a 1-inch-by-3-inch board between each of the wider boards the same way.
Cover each wall the same way. Cut the boards to fit around doors and windows as necessary.
If you're planning to paint the siding, prime the back of the lumber before you nail it up with the same paint, to minimise warping or cupping. You may also choose a durable wood like oak or cedar and leave it unpainted on both sides. Once you've decided on a gap between the boards, cut a scrap of wood that width as a spacer and place it between the boards to mark where to nail the next one. Nail the board on, then pull out the spacer and use it again. Choose wider or narrower boards and battens, as long as the battens overlap each board by at least 1/2 inch.