Clean out the expansion joint between the pool and the deck, using a nylon brush to remove any dirt or debris from within. Wash the inside of the joint with a mix of mild liquid soap and warm water, using the brush. While washing inside the joint, wash the two surfaces to either side with a sponge as well, extending from the joint edge about 4 inches. Rinse off the soap with clean water, and then pat the surface dry with a clean rag.
Measure the depth of the expansion joint, using a ruler, and then subtract ½ inch from the measurement. Purchase backer rod foam from a hardware or home improvement store with the same diameter as the modified depth measurement.
Stuff the backer rod foam into the expansion joint, pushing it to the bottom of the joint with the end of a flat-head screwdriver all along the perimeter of the pool. When in place, the foam should leave a space of about 1/2 inch in the expansion joint for adding the caulk. Cut the rod when necessary with a utility knife.
Place strips of masking tape along the surface of the deck and the pool on both sides of the joint. The tape will prevent the caulk from overflowing the joint area and will help you create a sharp caulk line.
Use an elastomeric sealant to caulk the joint. Pack the joint full to the surface with the sealant, using a trowel or caulking gun to press the sealant firmly into the joint over the foam rod. Go over the surface of the caulk with the flat of the trowel to level it out on the surface of the pool. It's fine if the caulk goes onto the masking tape bordering the joint.
Pull the masking tape from the sides of the expansion joint to create sharp edges to the caulking. Allow the caulk to dry for the length of time suggested by the caulk manufacturer before using the pool area.