-Make sure the tile and tub surface is cleaned and all the soap scum is removed. Not much sticks to soap scum. You can use a number of soap scum cleaners for this.
-Use a single edge razor blade in a holder to scrape off any old caulking and residue. I avoid metal putty knives because they leave marks on tile and porcelain tub finishes.
-Make sure the joint is cleaned of any loose debris
-Get a roll of 1-1/2" wide blue painter's tape and apply it to the walls approx. 1/16" - 1/8" on both sides of the inside corner. It will leave a tiny strip of tile showing between the blue tape. Press the tape into the tile so it sticks well. Don't press the whole width of the tape tight, just the inside edge so it peels off easier later.
-Do this tape thing for all the vertical inside corners.
-Cut the tip off the silicone tube so the hole is about 1/8". Start squeezing the caulking into the slit between the painter's tape. You don't need much because you will be removing most of it with your finger next so don't overdo it. ***Only caulk one joint at a time***
-Soak a rag in denatured alcohol, rub it all over the tip of your index finger and run your finger down over the caulking making it smooth. The alcohol keeps the caulking from sticking to your fingers. If you are in a pinch you can spit on your finger and it'll do the same thing. The alcohol is good to have around as it'll clean up wet silicone like nothing else in case you get it all over the place.
-Put the caulking gun down and immediately peel off the blue tape. Sometimes if you don't press hard enough the tape will leave a slight ridge when it's peeled off. Don't worry, it'll still keep water out but sometimes I just wet my finger and give it a gentle run down the joint just to smooth it out. Don't put much pressure on it and do it right away or it''ll drag the surface since it skins over so quickly. This is why you only do one joint at a time.
-The caulk-covered tape is a sticky mess so you should have a box or trash can handy to dispose of it right away.
-Once all the vertical joints have skinned over you can move to the horizontal joints.
Just remember to move quickly. Tool it once with your finger and leave it alone. I have caulked hundreds of feet of tub walls so let me know if you have any questions. Good luck!