So, Torture isn't all that useful due to the fact that its primary purpose is to break girls, and you want them unbroken for as long as possible due to breeding. That said, there is one girl where it becomes mandatory, and that's Lumine.
If you want to break Lumine, you can't just use the altar. You have to torture her repeatedly to get her element to break, then you can corrupt her. If you want her unbroken for the purposes of breeding, then you can ignore the mechanic (for now, we don't know if future NPC's will have similar requirements, such as Archons when we get them.)
In terms of how torture actually functions, you are trying to get elemental reactions. So just switch between hydro and dendro application repeatedly to create blooms so you can break down the character.