Dom skills are named Assertivness most of the time, so intitally you'll be able to raise these stats by:
1. Refusing to give pocket money to school bullies (choose 'shove your way past' when asked to give money)
2. Joining in or intervening when a student is harrassed by another during lessons.
3. Watching camgirl streams where randomly you'll see a video with Ds content
4. Winning a game bet at the Arcade and giving a spanking in reward.
5. Being active and defiant sexual during encounters: resisting changing positions, not asking (this increases submissivness, even if a male MC asks a girl to suck his cock after he's pulled it out of her ass. Yes, it is that stupid!) To put it simply, choose the red buttoned options, whenever you can.
As your sexual knowledge, assertivness/dominance and disinhibition grow, more dominant actions will become available (butt spanking, tit slapping, ball slapping and choking). But as the sex scenes are so underwhelming and the sex mechanics in their entirety are one huge work in progress, this doesn't change much. Participants act like soulless robots and you can spank the hell out of your sex partner and they won't give any particular reaction to that, whether they're into being rough-handled or not. The same with watersports: if you're into receiving those, just press your partner's bladder and they'll pee on you, like the digital rubber dolls they are... If you into peeing on others, it's even more random. Currently you can't use it as part of your dominant/sumbmissive act, you just piss/get pissed on and enjoy the smell afterwards, like that's all there is to it.
My guess is that the Library subplot involving discovering the-BDSM themed section will be expanded in future updates, allowing players to study and practice sadomasochism, including more serious impact-play, bondage, etc. instead of just being 'brutal' when fucking.