Never really liked how tech works in CK2.
Dunno if it could be more interesting if we got rid of the Cultural, Economic and Military points. Instead, every tech has separate points.
For example:
By constructing certain castle buildings, you increase Castle Infrastructure tech. Also, certain traits of Steward councilors, like Architect, will provide some bonus. Aside from stealing tech from others, those would be the only ways to increase Castle Infrastructure.
Same goes for every other Economy tech. By utilizing good councilors, and by actually constructing buildings, your knowledge for that technology increases.
Siege Equipment increases after every successful siege. Also when your Marshal has a trait associated with it.
Other military techs simply increase with every battle, and depending on which type of units you use the most.
Finally, Culture tech is a bit tricky. Perhaps they can be influenced by certain laws, or whether or not you are at war. Perhaps prestige and piety can have some influence...