Just go around town hanging out and working for people. Get sleep before you run out of a stat, then go while hanging out or working with people with scenes you've already seen, run out of that stat during it and you'll get a gameover and progress more of the story.
Getting a gameover reverts the day back to the start, and sleeping moves the day to the next, so make sure you always sleep before getting a gameover.
There are other ways of getting gameovers and scenes that require you to lose a stat somewhere else, or already have one of them at a certain amount.
And don't forget to have multiple saves.