Just read through the conversations until Sojiro drives you home. Another separate cutscene will play as well.
Spoiler:
It will be already evening by the time you arrive. Upstairs, Sojiro will give you a diary which will enable you to save your game by writing on it. There are only 16 save slots in the game and considering the variety of variables involved in the game, you’ll need all of those (and even more) to have enough backups to go back to in case you need to change some actions and decisions in the past. The game has a very limited and strict timeline to follow after all.
After Sojiro leaves, go downstairs and answer the phone. Head outside the shop and go back in again to flip the store sign. You can’t do anything else at this point but to go back to your bed and sleep.