Clean out the mortar joints between the stones using a masonry hammer and a tuck-pointing chisel or a small, flat cold chisel. Employ the tools gently to avoid damaging the stone. Remove all loose material to a depth of at least 3/4 inch, or two and one-half times the width of the joints. Work slowly and carefully.
Sweep the joints clean, then spray the area with water. Mix a small batch of mortar in a bucket according to the manufacturer's instructions. Add only enough water to the dry mortar to make a mix the consistency of peanut butter. Allow the mortar to slake for 15 minutes, then mix again to incorporate any water that collected on top.
Spray the foundation wall again if necessary to dampen the joints. Use a brick trowel to scoop up and hold the mortar beneath each joint while pushing the mortar into the joints with a pointing trowel. Fill the joints, then scrape off any loose mortar clinging to the face of the stone. Allow the mortar to firm up in one section while you move on to the next.
Smooth each joint with a tooling jointer once the mortar is firm to the touch. Clean the face of the stone of any loose material by gently brushing at a diagonal across the joints so you don't pull out the fresh mortar.
Clean any cement stains from the stone using a sponge if desired, then allow the mortar to set for several days. Once a day, mist the foundation to keep the stone and joints slightly damp. Protect the wall from any harsh weather if necessary by covering it with a tarp.