Sweep the surface surrounding the crack with a stiff bristled broom to remove any dirt or debris. Clean out the crack itself with a nylon brush, emptying the crack completely so that you can access the crack bottom and sides.
Run a crack chaser blade through the crack to even out the crack edges and to create a somewhat level base to the crack. While there's no need to create a completely level base, you should attempt to create a base that doesn't change by more than 1 inch. Make the sides of the crack smooth horizontally, but angle them slightly wider as they descend to the base of the crack to provide an undercut for the patch to grab onto. Remove any concrete residue from the crack with the brush, and then clean the crack out with a hose. Wait about three hours for the crack to dry out after cleaning.
Use a putty knife to apply a light layer of epoxy adhesive over the sides of the crack and along the crack bottom. Allow the adhesive to dry long enough to lose its wet appearance while retaining its sticky surface. The adhesive will help bond the new patching material to the old concrete.
Cut the top from a tube of epoxy resin, and then inject the resin into the crack, filling it up to the surface of the concrete. Scrape off any excess resin to level it off.
Pour an aggregate matching the existing aggregate onto the patch. Spread it around evenly using a wooden craft stick, then pour epoxy onto the aggregate to hold it in place. Wait 24 hours for the patch and aggregate to set.
Spray concrete sealant over the patch area to add waterproofing to the patched surface. Wait another 48 hours before using the patched area as normal.