Cut away the old caulk using your razor knife, running it along both edges of each caulk line and getting it all out.
Wet the toothbrush with bleach and scrub the exposed lines thoroughly, removing any residual material. Rinse well. Let it dry overnight.
Load your caulk gun with its caulk tube. Cut off the pointed end of the tube, making a ¼-inch hole there. Push your 3-inch nail into the hold to break the seal inside. Squeeze the trigger until caulk starts coming out the end.
Hold the tip of the tube against of the exposed lines, at the end. Squeeze the trigger again and begin moving the gun along the line, laying the caulk line. Keep it as smooth and even as you can. Continue to the end of the line.
Release the trigger and raise the gun off the surface.
Wet your thumb and run it over the new caulk, pressing it gently into a flat, straight line.
Repeat for each of the caulk lines. Let it set for 24 hours before using the shower.