Brush out the gaps with a stiff brush and vacuum out any dirt and debris to ensure the gaps are dry and clean.
Lay foam or cork backer rod over the length of the gaps and mark the length of the gap on the backer rod with a permanent marker. Double check your measurement with a tape measure. Use a utility knife to cut lengths of backer rod to fit each gap.
Press the foam or cork into each gap with your hands or the back end of a hammer. Once in place, it should be about 1/8 inch from the surface of the concrete.
Load a tube of concrete joint sealer into a caulk gun. Squeeze the sealer over the foam or cork expansion joint and spread the material smooth with a trowel or gloved finger.
Position the end of the caulk gun over gaps that are too small to fill with foam or cork. Squeeze a line of sealer over each gap and smooth it down with a gloved finger. Wait for the sealer to dry for a day and add a second coat to ensure water will not be able to seep through.