Install and grout your shower tile, grouting only the flat spans and not the spaces along the inside corners between the walls and around the edges of the floor. Run your putty knife inside those lines to remove any stray grout that gets in there. Let the grout set for 24 hours.
Load your caulk gun with a caulk tube. Cut off the tip of the tube with a utility knife, making the cut at 45-degree angle with a 1/4-inch hole.
Pierce the inner seal of the caulk tube by pushing a 3-inch nail into it. Squeeze the caulk gun's trigger to expel a little caulk from the end. Press the pressure-release button at the end of the gun to stop the caulk.
Place the tip of the caulk tube onto one end of the first lines you're going to caulk, holding the gun at roughly a 45-degree angle, so the cut at the end of the tube is sitting flat on the line.
Squeeze the trigger of the gun to start the caulk flow. Pull the gun slowly backward along the line, filling it with caulk in a smooth bead. Stop the flow at the end of the line by pressing the pressure-release button.
Wet your spoon by holding it under water from the sink faucet. Run the back of the spoon along the caulk line, from beginning to end, to get the line flat and smooth in the corner.
Repeat for each open line. Allow the caulk to set for 24 hours.