Rinse the concrete steps well to give the mortar a clean base.
Dry set pieces of flagstone on the steps to see what pieces work best. Allow a similar amount of space for the joint. Since the edges of flagstone are irregular, the joint size won’t be uniform. Each stair tread should over hang by about 1 to 1 1/2 inches.
Cut straight edges for the flagstone steps with a masonry saw equipped with a diamond blade. Cut smaller pieces and the front edge with a hammer and chisel. Score the flagstone by tapping it with the chisel on both sides. Once you get a line marked, tap the flagstone with the hammer to break it.
Mix 2 parts masonry sand with 1 part Portland cement. Add enough water to make a stiff mixture that adheres to a trowel when you turn it over.
Lift a stone up. Pour some water over the concrete base to moisten it. Put some cement on the concrete step and smooth it out with a trowel. Set the stone back into position. Continue setting the stones on the step following this procedure. Adjust the amount of concrete under stones of varying thicknesses to keep the surface of the steps the same height. Wipe each stone lightly with a clean, damp sponge as you go to remove any concrete on them.
Repeat this process until you have all the stones set on the steps. Allow the concrete to dry overnight.
Mix 2 parts masonry sand with 1 part Portland cement. Add enough water to make a stiffer mixture than you had in Step 4.
Use a tuck pointer or grout bag to insert the concrete mixture between the joints. Wipe off any excess concrete with a clean, damp sponge. Allow the concrete to dry overnight.
Mix 1 part stone cleaner with 10 parts water. Scrub the flagstones with the cleaner. Allow the cleaner to set on the stones for a few minutes to soak off any remaining concrete, then rinse well with clean water.