Clean out the hairline crack. Brush out any debris or dust.
Moisten the crack area for several hours prior to applying grout. This will prevent the concrete from drawing moisture out of the grout.
Apply the grout, using a putty knife or trowel. Put as much grout as possible into the crack, and smooth it so it is level with the surrounding concrete.
Cover the patched area with a plastic sheet after it has first been allowed to dry for a few hours.
Maintain the plastic sheet covering for about five days. Throughout this period, gently sprinkle the area with water daily.
Enlarge the crack, using a hammer and chisel. Make the crack at least 1 inch deep, and make the crack wider at the bottom than at the top.
Clean the crack thoroughly. Use a wire brush and garden hose or air pump to blow out all the dust.
Brush concrete adhesive into the crack. This will help to hold the concrete patch in place. If an adhesive will not be used, thoroughly moisten the concrete.
Tamp the concrete patch into the crack. Fill the crack completely, and smooth the patch down with a trowel or wooden float once the mixture begins to set.
Allow the patch to dry for about two hours before covering it with plastic sheeting. Keep the plastic sheeting over the patch for about five days, lightly wetting the patch daily during this period.