Someone else may be able to provide a more exact list, but the main ways seems to be:
1. Periodically, galactic events will give you a point automatically, or give you missions to build certain buildings that provide a culture point.
2. You can hire leaders that give "+1 culture point" upon recruitment. They are often expensive compared to their stats.
3. You can build certain buildings in the tech tree that give you +1 culture point. Some examples include the worldheart borehole in the "deep core mining" research, the Tower of Endless Night in the "espionage" research, and the culture ministry research (no building required) among others.
There could be more ways I'm not remembering. With that said, culture/ideology points are somewhat rare, and you don't get a whole ton of them.