Clean the surface of the concrete with a solution of 1 part household bleach and 10 parts water. Wear rubber gloves and use a bucket to transport the mixture. Use a scrubbing brush to remove all of the dirt and debris, then rinse it thoroughly with a hose.
Place the flagstones over the concrete after it dries. Position the flagstones as desired and use chalk to mark any stones you need to cut. Cut the stones with a rock hammer and a chisel, and wipe off any dust left behind with a cloth.
Combine 1 part cement powder with 4 parts fine sand and enough water to give create a stiff consistency.
Remove the stones from the concrete and place them within easy reach. Spread a 1/4-inch layer of sand mortar over the concrete with a trowel, and 1/4-inch layer over the bottom of the flagstone.
Set the first flagstone in place, pressing it gently into the sand mortar. Continue setting the stones according to your pattern, using plastic spacers to ensure consistent spacing between each. Set a water level over the stones and use a rubber mallet to press the stones deeper into the mortar as necessary. Use a clean cloth and the edge of the trowel to wipe off excess mortar and splatters as you go. Wait 36 hours for the mortar to set.
Combine 1 part cement, 1 part fine sand and enough water to make a stiff consistency. Remove the plastic spacers and fill the joints between the stones using the trowel. Wipe off excess grout as you go. Smooth the joints with a concave jointing tool to create a smooth surface between the stones.
Cover the flagstones with a plastic sheet for a week to protect the new surface from weather and foot traffic. Water the surface two times a day to increase the durability and look of the grout.