Tear out the wooden steps with a pry bar or crowbar. Be careful of nails protruding from the wooden pieces.
Dig a hole for a 6-inch foundation where the stone and concrete steps will be, if a foundation does not already exist. The foundation should be as wide and long as the stairs themselves, and 6 inches deep. Tamp the ground with a tamper to make it even. Line the perimeter of the hole with wooden boards if the soil around the edge of the hole is crumbling or not compact.
Pour wet concrete into the hole and fill it halfway. Lay steel rebar into the hole in a grid fashion and then fill the rest of the hole with wet concrete.
Level the top of the concrete with a squeegee and then let the concrete cure according to the manufacturer's instructions.
Remove the boards from the foundation, and fill in the edges of the hole around the concrete with soil.
Spread the wet mortar over the concrete foundation and lay the first course of concrete blocks. Spread the sides and backs of the blocks that will form the joints between adjacent blocks with mortar. These blocks will make up the first step of the staircase. Leave a space at the front of the course wide enough for a layer of bricks.
Spread mortar over the top of the first course of concrete blocks, beneath the location of the second course. Remember to leave an open space at the front of the second course, to form the top of the first step. Each subsequent course will be set back from the course beneath it, leaving a space the width of one step.
Finish laying the final course and scrape the excess mortar from the joints with a trowel. Wait for the mortar to cure according to the manufacturer's instructions.
Spread mortar on the concrete foundation in front of the first course of concrete blocks. Lay the first course of brick over the wet mortar. Spread the bricks with mortar on the sides and backs that lie adjacent to other bricks or blocks.
Scrap excess mortar from the brick joints with a trowel.
Spread the top of the first course of brick with a trowel and lay the second course of brick. Start the second course with a half brick, and then use full-sized bricks, to stagger the placement of the bricks. Spread the backs and sides of bricks that lie adjacent to other bricks with mortar.
Continue to build up the bricks in front of the concrete block staircase until you reach the top of the first block.
Spread the top of the first step with wet mortar. Lay flat paving stones on the mortar and use a trowel to spread the joints between the stones with mortar.
Scrape excess mortar off of the staircase with the trowel.
Continue the process of laying bricks in front of the concrete blocks and covering each stair with flat paving stones until the entire staircase has been covered with brick and stone veneer.
Wait for the mortar to cure and then scrub the new staircase with a stiff bristle brush to remove excess mortar dust and chunks of mortar.