Relationship level increases as the story progresses.
There is an event when the requirements are met, and the event increases relationship level. Examine the Misc Info screen, those girls with exclamation mark have an event available. Talk to the girl at her door or try to find where she is and meet her there. Some events happen at a specific time of day. Some events trigger without you doing anything. I think a girl can not have two events in the same day, and some events cause a multi day wait before next event for that girl can happen.
The game tries to explain these things. You can read the Wiki to find out more, or just experiment.