Run a sharp razor blade or utility knife along the top and bottom lines where the old sealant meets the bathtub and the wall. This will loosen the bond between the old seal and the bathroom installation. You must remove the old seal before you can replace it.
Dig out all of the old sealing caulk using a scraper or utility knife. Be very careful not to scratch your walls or bathtub, as these scratches are not easily removed. Dig until all old sealant is removed. Any leftover sealant will create a weak point in the new seal.
Dampen a rag in rubbing alcohol, mineral spirits or a similar solvent cleaner. Wipe out the entire area that you will reseal, as well as the bathtub surface below. This cleaner will remove any remaining small pieces of old sealant.
Clean the area with bleach or a commercial mold killer if you see any mold or mildew in the sealant area. Mold left in there before you apply the new caulk will continue to grow and damage your walls, as well as undermining the new seal. Allow the area to dry completely before continuing.
Run a line of painter's tape along the top of the tub, as well as the bottom of the wall piece, creating a little valley for the caulk. This will help you get a cleaner finish for the caulk without spilling it everywhere.
Cut the tip of the caulk dispenser at a 45-degree angle to create a small, angled hole. This will ensure that only a little comes out at a time, reducing your chance of making a mess. You can cut the hole bigger as you become comfortable with it if you want to go faster.
Run a steady, thin bead of caulk between the two pieces of tape to fill in the gap. Do one side of the tub first. You must complete the following steps while the caulk is still wet.
Wrap a small piece of damp paper towel around your index finger. The damp towel stops the caulk from sticking to your finger instead of the wall and tub. Gently press the wet caulk into the seam, firming it in place. Add more caulk if necessary to fill the gap completely and press again. Continue until the gap is sealed completely.
Remove the painter's tape while the caulk is still wet. The caulk will expand as it dries to fill in the small gaps left by the paint. Repeat the procedure for each side of the tub, until all gaps are sealed with caulk.