caulking
I've just got a tube of XtraBond250 sealant with a threaded nozzle. It's not at all clear how to get started. Do I puncture the tube at the male threaded end? Or cut off the conical portion of the the threaded part? Or …? And then how to seal it back up when I'm done in case I need more in the future?
If there is moisture still there, then mold and mildew will return. If the problem was not fixed, then it will return. Bathrooms are particularly bad in this respect, since moisture is a natural consequence of using water. I would expect to need to redo things like caulking every few years to fix this. It will not last forever.
Scrape/pull off the old silicon.
Apply a solution of bleach to kill the mold. Be careful when you apply it, as bleach can damage the clothes you are wearing. Keep the area ventilated well.
Let it dry. If you are in a hurry, a fan blowing on the area will help. A hair dryer can also speed that process considerably.
Apply new caulk in a smooth bead. I use my finger to spread it along the joint. Definitely use a high quality silicon caulk with a mold/mildew inhibitor. These are caulks that are designated for use in bathrooms.
Allow it to fully dry before you get it wet again. Give it a day or so. It will skin over in an hour or so, but make sure it has properly cured before use of the shower.
Expect to redo this process in some number of years. The exact time it will last depends on how well the area is ventilated.
Of course, there may be mold in the wall itself. This is difficult to deal with unless you tear the wall down to replace it completely, and even then water tends to attract the stuff. Mold spores are everywhere.
In addition to DA01's suggestion, there are also smaller tubes of caulk that may be thin/small enough to angle into the casing corner. More costly, but you only need a little (if it fits).
Best Answer
Cut off the tip of the conical stub. Doesn't much matter how large the opening ends up being, but don't go past the tapered part. There's no reason to do so.
Then, start with the smallest opening on the nozzle that you think will do the job. Less caulk is better, and you can always open it further.
To seal it, I typically wrap tape around the end of the nozzle in a cylinder, pinch the end closed, and squeeze caulk into it. This creates a self-sealing plug that can be easily pulled off later.