Use a wire brush to scrape away loosened or pointed edges of the crack. Sweep or vacuum up debris with a wet/dry vacuum.
Wear goggles to protect yourself from shrapnel and use a chisel and hammer to undercut the crack. Expand the crack to at least an inch deep. Chisel the bottom of the crack so it looks like an upside down V, with the bottom wider than the top. This will help spread the patching material into the crack.
Sweep or vacuum all debris from chiseling so the area is free of dust. Dampen the crack and the surrounding edges with clean water, but do not let water settle into the crack. There should be no standing water in your repair area.
Mix 3 parts sand and 1½ parts Portland cement with enough water to form a thick, creamy mortar. You can also use a pre-manufactured cement or concrete patch. Mix with a shovel or power mixer in a bucket or wheelbarrow. The actual amount of water needed will vary based on your chosen products as well as the temperature and humidity of the area.
Spread the cement mixture into the crack, using a mason's trowel. Force it into the undercut areas first, then fill the crack. Scrape the flat edge of your trowel back across the surface to remove any excess that runs over the sides.
Cover the patch with plastic wrap and allow it to cure fully--generally two or three days. If you used a manufactured product, follow the manufacturer's instructions regarding drying methods.