Clean the concrete deck thoroughly with a pressure washer, garden hose -- or scrub with detergent and water and rinse with plain water to remove all grime and debris. Allow the deck to dry.
Cut off the end of the tube of caulk on a diagonal with the utility knife. The opening should be no larger than the width of the crack. Pull the plunger back in the caulking gun and place the tube inside.
Cut off a length of foam backer rod as needed for the length of the crack. Foam backer rod is available in a variety of widths. Use a width that is one size larger than the crack to ensure a tight fit. Push it firmly down into the crack to a depth of one-fourth an inch below the surface of the deck if possible. Apply the caulk on top of the backer rod. If the crack is thinner than half an inch, skip this step and apply the caulk directly to the deck.
Place the tip of the caulk at the start of the crack. Pull the plunger and release the caulk, drawing the caulking gun along the crack.
Smooth the caulk down with the back of an old spoon, or wet your gloved finger and move it along the length of the crack.
Sprinkle some dry cement along the length of the crack. The cement will stick to the caulk, making the repair less visible from a distance once the caulk sets.