You have to clean the surface of the concrete before anything else. Clean with a washer that is at least 4,000 psi careful to follow manufacturer’s instructions to avoid damaging the concrete with the pressurized spray.
Using a small cold chisel or flat-head screwdriver dig out rubble in large cracks and chips. Loosen dirt and debris in small cracks using a wire brush. Sweep the area or use a wet/dry vacuum to remove all remaining debris.
Using a masonry trowel fill all small cracks and chips making the surface smooth. You should allow the patching compound to cure according the manufacturer’s directions.
Should there be damage at the front edge of the step, clean it as follows. Place a board in front and secure it in place with bricks or concrete blocks. Wet the damaged area and fill it with patching compound. Using a masonry trowel smooth the patch and then allow it to cure thoroughly.
Spread a layer of isolation membrane over the concrete using a notched trowel. You should smooth the surface of the membrane using the flat edge of a trowel. Making sure to follow manufacturer’s instructions, allow the membrane to cure.
When tiling a stairway with landing the sequence is important. Your main goal is to install the tile in a manner that the least possible cut edges are visible from the main viewing position. If you are tiling the sides as well, start there first. Start by extending horizontal lines from the top of the stair treads back to the house on the sides of the steps. Use a 4 ft level.
Prepare a batch of thinset mortar with latex bonding adhesive and trowel it onto the sides of the steps, trying to retain visibility of the layout lines. Because the top steps are likely more visible than the bottom step, start on top and work your way down.
Begin setting tiles into the thinset mortar on the sides of the steps. Start at the top and work your way downward. Try to lay out tile so the vertical gaps between tiles align. Use spacers if you need to.
Wrap a 2 x 4 in old carpet and drag it back and forth across the tile surfaces to set them evenly. Avoid getting too aggressive as you dont want to loosen all of the thinset mortar.
Measure the widith of a riser, making account for the thickness of the tiles you have laid on the sides. Calculate the centerpoint and mark it clearly with chalk or a high visibility marker.
You will then dry lay the tiles on the stair risers. As the location of the tops of the riser tiles affects the positioning of the tread and landing tiles, you will acheive the most accurate layout if the riser tiles are laid first. Vertically stack the tiles against the riser, note that in some cases you will only need one tile to reach from tread to tread. Add spacers. Trace the location of the tread across the back of the top tile to mark it for cutting.
Cut enough tiles to tile all of the stair risers. Be sure to allow enough space for grout joints if you are stacking tiles.
Mix thinset mortar with bonding adhesive and trowel the mixture onto the faces of the risers. You should be able to tile each riser all at once.
Carefully lay your tiles on the risers with the bottom edges resting on the tread and the top edges flush against or slightly lower than the plane of the tread above.
Dry lay tile in both directions on the stair landing. Maintain the same grout lines that were marked by the riser tiles, meanwhile evaluating the front to back layout to make sure you don't end up with a row of tiles that are less than 2 inches or so in thickness.
Using the measurements indicated by your dry run, cut your tiles for the landing and install them first by trowelling thinset mortar for the bullnose tiles at the front edge of the landing. The tiles should overlap the top edges of the riser tiles, but should not extend past their faces.
Set the first row of field tiles, maintaining an even gap between the field tiles and the bullnose tiles.
Add the last row of tiles next to the house and threshold, cutting them as needed so they are between ¼ and ½” away from the house.
Install the tiles on the stair treads, starting at the top tread and working your way downward. Set a bullnose tile on each side of the centerline and work your way toward the sides, making sure to conceal the step-side tiles with the tread tiles.
Fill in the field tiles on the stair treads, being sure to leave a gap between the back tiles and the rise tiles that’s the same thickness as other tile gaps.