Put on safety goggles, work gloves and a respirator equipped with an N-95 filter.
Direct a stream of water from a high-pressure nozzle attached to a garden hose at the stairs washing off excess concrete dust. Wetting spalling concrete helps keep silica dust from becoming airborne.
Equip a hand-held grinder or power drill with a wire brush attachment. Begin on the top landing and grind the spalling surface, removing loose concrete. Work from the top of the stairs down, grinding the spalling surface until the top layer of concrete is removed from all steps.
Spraying the steps with water washes off concrete dust, flakes and chips. Let the concrete stairs dry.
Pour a commercially available concrete patching material containing Portland cement, sand and polymers into a trough or bucket. Stir the dry ingredients with a hoe. Create a mound of patching material and dig a hole in the center with the hoe. Measure water according to the manufacturer's directions and pour it into the hole’s center. Pull the dry patching material into the water with the hoe until the concrete patching material forms the consistency of a thick paste.
Pour an epoxy-based concrete sealing, setting and bonding agent into a small bucket. Dip a paintbrush into the sealing, setting and bonding agent and paint a coat over the landing.
Scoop up wet patching material with a concrete-finishing trowel. Sweep the patching material over the wet epoxy in wide arcs with the concrete-finishing trowel covering the rough concrete. Continue applying patching material over wet epoxy until a smooth layer of the patching material covers the landing.
Paint the sealing, setting and bonding agent to the steps one at a time beginning with the top step. Apply the patching material over the wet bonding and sealing agent and smooth the step with the concrete-finishing trowel. Continue applying sealing and bonding agent and troweling patching material over it until all steps are covered.
Block the stair entry with a barricade or caution tape for 24 to 72 hours while the concrete patching material cures.