First off, I want to warn you that sealing around anything with silicone sealant is tricky. Without a few pointers, things can go wrong very quickly and you'll end up with your hands covered in sealant which is nigh on impossible to get off once dried. Also, I want to mention at this point that silicone sealant is known to cause mouth cancer so make sure you wash your hands thoroughly afterwards.
Using silicone to seal your bath is nevertheless something anyone can do and although you might mess it up the first time, you can try it as many times as you need to. It's also something that you get better at with practice so it's definitely worth learning.
Tube of silicone sealant
Caulking gun skeleton
Stanley knife (if replacing old sealant)
White spirit (if replacing old sealant)
As with most things, there's a bit of preparation work you have to do before you can start. If you're replacing old sealant that has either gone mouldy or split, you're going to have to remove it completely before applying new silicone. There are specific tools designed specifically for this but you'll probably get away with just a sharp Stanley knife. Cut vertically and then horizontally to remove the old sealant and then scrape away any that's left behind.
Silicone won't stick to any surface that's either wet or greasy. That's why you're going to have to wipe down the area with a solvent like white spirit or rubbing alcohol to remove any soap residue and body fats. Once this is done, wipe off the solvent with a paper towel (try to avoid skin contact) and then leave it for 5-10 minutes to dry fully. Tea break?
An important trick of the trade in sealing baths is that the you should fill the bath up with water. A standard bath full of water (and a bather) can weigh 150kg which is enough to cause the bath and the floor to flex under the weight by a couple of millimetres. Silicone is flexible but not flexible enough to stretch this far and will split either immediately or over time as it dries out. Filling the bath with cold water is just as good as warm (actually slightly better) but make sure the water doesn't splash and make the surface that will be receiving silicone wet.
Now you're ready to start. If you've never used a skeleton gun before, familiarise yourself with it by feeling how much pressure it requires on the handle and how to release the pressure quickly if needed using the release switch. Next load the gun with your tube of silicone sealant and pull the trigger a few times until it comes into contact with the end of the tube. Then cut off the tip of the nozzle (a smaller opening is far easier for beginners to handle) and poke a long nail into the tube to break the seal.
The key things to focus on in applying sealant are control and consistency. A continuous flow of silicone is necessary for a good finish so you should be aiming to apply the same amount of force to the trigger throughout. Don't worry too much if there are any small areas with not enough or too much silicone, just make sure to apply a thin bead along the whole stretch. The thickness of the silicone of course depends on your particular bath and tiles but is typically around 3mm.
Once you've gone all the way round the bath, you're ready to start smoothing the silicone. Be sure to flick the tab on the skeleton gun to release the pressure on the tube, then grab an old sponge or towel and dip it in the bath. We're going to be smoothing the silicone with our finger and we need to make sure our finger is wet while we do this to achieve a smooth finish and to stop the silicone from sticking to our finger.
Run your wet finger along the bead of silicone applying a fair amount of pressure but not so much that the silicone squeezes out the sides. If you find it squeezing out the sides no matter how little pressure you're applying, your silicone is probably too thick and you'll need to start again. Wipe off any excess silicone that builds up on your finger on the towel as you go, then wet your finger again and continue where you left off. Remember not to wet your finger by licking it because as mentioned earlier, silicone is known to cause mouth cancer.
Hopefully, you should have a pretty nice seal now between your bath and your tiles with a nice, smooth finish. If not, don't worry because as I said at the start, it's one of the tricker parts of DIY and takes practice. You have enough silicone in a tube to try this around 5 times so there's no harm in waiting for it to dry, cutting the sealant away and starting from scratch. Chances are that the problem was that you applied too much silicone. It's hard to judge the first time you do this but just remember, less is more.