Cut out the old caulk from around the perimeter of the shower floor, using a razor knife. Run the knife along the top and bottom of each caulk line to separate it from the tile behind it, then push your putty knife forward under the putty to get it out.
Fill a spray bottle with 1 part bleach and 3 parts water. Spray down the joint lines where the caulk was. Let it dry for an hour.
Put a caulk tube into your caulk gun. Cut the end of the tube off with your razor knife, at a diagonal angle, so it creates a ¼-inch hole at the end.
Slide a long nail into the hole to break the seal inside. Squeeze the caulk gun trigger until the caulk rises up in the tube.
Set the tip of the tube onto the first line, at one end. Position the caulk gun at a diagonal angle back from the line.
Continue squeezing the trigger so it expels caulk onto the line. Drag the gun back along the line to lay a straight, smooth line from end to end.
Lift the gun away from the line at the end. Wet your thumb and press it lightly along the caulk line, smoothing it out.
Repeat for each span around the shower floor. Let it set for 24 hours before using the shower.