In Persona 4 Golden, several days will automatically pass by naturally alongside the story. However, many other days are left completely up to you to do whatever you want! A day is split into several sections that may or may not allow you to do things.
School days may consist of:
Early Morning (Dialogue)
Lunch (Spend Time)
Afternoon (Pop Quiz)
After School (Spend Time)
Evening (Spend Time)
Days off usually consist of:
Most of the time After School and Evening are the only times you can truly do something. You can either spend the Afternoon / After school doing Side Quests, improving a Social Link, buying things, or searching inside the TV world.
After specific things are done to pass time, or going directly to Dojima Residence, it will turn to the Evening. When it’s the Evening, you can talk to Nanako, Dojima (if he’s home), read a book, make a Boxed Lunch, or work on the Garden. If Dojima isn’t home, you can sneak out and do a little more shopping or possibly improve more Social Links. However, if you were inside the TV during the Afternoon, you will be too tired to do anything for the evening.
Things that make time pass by
There are a number of things to do that allow time to pass by.
Spending time with friends
Exploring a dungeon in the TV World
Participating in school club activities
Completing Mysterious Fox Quests
Drawing a Fortune from the Shrine
Fishing at the Samegawa Flood Plain or Shichiri Beach