Concrete is porous and will soak up all of the water it can. Rehydration of concrete steps can cause the steps to decay prematurely. To combat this, some people paint their concrete steps with epoxy sealer. However, due to the high moisture content in concrete, if you paint your concrete steps, you should plan to do so every few years because the existing paint will come off if the concrete remains exposed to water.
Scrub all the old loose paint from the surface of the concrete steps with a metal wire brush. Sweep the paint off the stairs as needed with the broom. If you have any cracks in the concrete, scrub the paint away from the cracked areas with the wire brush.
Patch any cracks in the concrete with mortar and wait at least 24 hours for the patching to dry. Once dry, go over the patching with an orbital sander to smooth the mortar so it blends in with the concrete.
Clean the surface of the stone with a stone cleaning solution such as muriatic acid mixed with water. Use a scrubbing sponge to remove any dirt and debris. Allow at least 24 hours' drying time before moving on.
Apply two coats of epoxy masonry sealing paint. Use a paintbrush for harder to reach areas such as where the steps meet with unpainted walls. Use a paint roller for large flat areas. Allow 24 hours between coats.