Skill and ability points can be freely spent on available skills and abilities (those unlocked by origin, faction, etc.) for the character. No teachers are required for this, even if it's a special technique or ultimate ability. If desired, you can role-play this moment with one of the practitioners of that ability, or write that the character practiced based on information from other sources (e.g., someone showed the training method, and the technique was only mastered now), but this is not mandatory – you can simply choose what you want without writing anything.
However, there will also be other special techniques, individual skills, and improved versions of the abilities presented on the first page – these will have to be unlocked from the corresponding masters and subsequently purchased with points.