Remove the crumbled pieces of concrete around the area you need to repair. Remove excess around the area with a hammer and chisel to ensure that you have removed any weak pieces close to the area. If the crumbling goes below the surface, use a circular saw with a stone blade to cut out the crumbled area quicker than with the hammer and chisel. Remove the debris and clean the area with a broom.
Mix cement and water in a bucket with the drill and paddle, adding enough water to make a soupy, paintable mixture. This is known as a slurry mixture. Cement is a basic ingredient of concrete, and you are patching the area with slurry first so that you have a sticky layer to which the concrete mix can stick. Also mix some concrete mix in another bucket, adding water until you have a thick, peanut butter consistency.
Paint the slurry over the area with the paintbrush. Cover the entire area, including the sides and up over the top of the existing concrete. Pour your concrete mix on top of the slurry coat. Smooth it with a flat trowel to match the surrounding concrete. Let the mixture dry for 72 hours before allowing foot traffic or vehicle traffic.