1. Make sure you have everything to hand before you start. You will need plenty of masking tape, a sharp knife, kitchen roll or dry cloth, a cartridge gun, a cartridge of kitchen- or bathroom-grade silicone sealant and possibly a cartridge of silicone sealant remover.
2. Use the knife to cut and scrape away the old seal. Work gently, a bit at a time, and keep your fingers behind the blade - this way if you slip you won't cut them. If you prefer you can buy a chemical silicone sealant remover to do the job.
3. Use a dry cloth to clean the joint. The new silicone needs dry surfaces to stick to. Thoroughly clean the worktop/ bath and wall tiles with a dry cloth or kitchen roll; don't use kitchen or bathroom cleaner as some could get left behind and mess up your work.
4. Use the masking tape to protect the areas around the seal. Take time to get this right - the look of your finished joint depends on it. The areas you leave showing will be the areas the silicone will stick to.
5. Using the knife, cut the cartridge nozzle to the right size. At an angle of 45 degrees, cut the tip of the cartridge to open it and screw the nozzle on. Use the cartridge gun to squeeze out the silicone until it reaches the end of the nozzle. Wipe that off. Run a bead of silicone into the joint, sqeezing the gun and pushing the nozzle slowly along the joint. Once you've put it all in, lift the masking tape gently away.