In order to loosen up old caulk so that it can be replaced, apply caulk softener and let it sit for about 2 hours. When the old caulk is fairly loose, remove it with a putty knife or 5-in-1 tool.
To prevent mildew formation, clean the work area with rubbing-alcohol. Be sure to remove all soap residues and allow enough time for the work area to dry completely.
To ensure strength of the seals, completely fill the bathtub with water.
Load tile caulk in a caulking gun. Cut the tip of the gun at an angle of 45 degrees.
Start caulking one of the short walls. Make sure you keep the gun moving at constant speed while it is being squeezed. Move the gun in a direction opposite to which the gun is pointing. You may need to use a paper towel to clean excess caulk between applications. To prevent pooling, release pressure on the caulking gun as a corner approaches. Caulk along all other walls in a similar manner.
When you are done caulking the bathtub, smooth out the silicone line by running a wet finger over it and thus remove excess caulk as well.
Allow enough time for caulk to dry completely.