Scrub the expansion joint with a wire brush to knock dirt and other debris loose.
Clean the expansion joint with a vacuum cleaner. For best results, use the hose attachment for the vacuum and run it over the entire expansion joint to suck out all loose debris.
Fill the expansion joint with backer foam rod so the foam is 1/2 inch deep. The foam provides support to the caulk and is soft enough that it allows room for expansion. The diameter of backer foam rod needed depends on the size of the expansion joint, but 1/2-inch backer rod works well in most cases.
Line the top edges of the pool deck with caulking tape, right along the expansion joint. This prevents messes from caulk overflow.
Secure a tube of elastomeric caulk in a caulk gun. Pool supply stores carry elastomeric caulk specially made for pool expansion joints.
Move to one corner of the expansion joint. Stick the tip of the caulk tube at the surface of the expansion joint and pull the trigger gently until the caulk comes out.
Move down the joint while you squeeze the caulk gun trigger with an even pressure. The caulk should reach as low as the backer foam and come up just to the surface of the pool deck. Use this technique until the entire joint is filled with caulk. Allow the caulk to dry for at least 48 hours until you swim in the pool again.