Clean around the joint line to guarantee proper adhesion of the caulk. Remove any old caulk by slicing the large chunks away with a utility knife and dissolving the remaining bits with a citrus-based solvent. Scour any rust spots with a wire brush. Wipe down the area with a rag dampened in hot water. Avoid washing the vent with large amounts of water, as the water can enter and become trapped in the open joint. Allow the joint to dry completely before applying caulk.
Cut off the tip on the nozzle of a caulk tube, making the cut at a 45-degree angle. Stick a long nail or stiff wire down the nozzle to puncture the seal on the caulk tube. Load the caulk tube into the cartridge of a caulk gun. Secure the plunger of the caulk gun against the back of the caulk tube.
Hold the caulk gun at an angle and place the tip of the nozzle somewhere along the joint line, with the angle of the cut conforming to the surface plane. Pull the trigger to begin extruding caulk. Extrude an even bead of caulk along the joint, pulling the gun backwards at a slow, steady pace.
Force the caulk into the joint and smooth down the new seal by gliding a finger along the top of the entire caulk bead.
Allow the caulk to dry completely.