Fill the joints that need caulk with the foam backer rod. Cut the rod with the utility knife to the lengths required by the joints and add as many layers as necessary to fill the joint up to roughly three quarters of its depth, leaving the last portion for the caulking. Pack the backer in loosely, not tightly, as you do not want it to expand later and push the caulk out of the joint.
Trim the tip of your caulking tube down to match the width of the joint. Most tubes have predesigned lines in the tip that show you where to cut, but if not you can trim it down with the utility knife until it just barely slides into the grout joint without applying force or pressure. Insert the tube into the caulking gun.
Insert the tip of caulking tube into the joint and pull the trigger on the gun. Fill the joint slowly so you can ensure that the caulking is surrounding all of the foam elements behind and not leaving any voids that will cause pinhole air bubbles later on. Move your way across the joint. Wipe any excess caulk from the face of the tile with a damp sponge, but do not use too much water, as this will taint the caulking.