Here you will find all the information you need to know about dating/having best friends.
Getting people to like you
The first step in a relationship is to make friends. You can become friends with people by sitting with them in class, hanging out with them, talking to them, giving them their favourite flowers, and sending them letters.
After you've become friends with your chosen character, you want to continue increasing your friendship using the steps above. If rumours about the two of you start, you're heading in the right direction.
After a few days, with enough interaction, your chosen character should ask you to meet them at Lover's Point at a specific time. The default is 6:00pm/am, but if you say 'that won't work' then a few options will be presented to you for alternative times.
Meet them and they'll give you a nice line of dialogue about enjoying spending time with you and then ask you to hang out.
Congratulations, you've succeeded in advancing your relationship!
What Happens Now?
Now that you're in a relationship, your chosen character will ask you to play more often, deliver cute lines of dialogue, and send you frequent letters.
You never touch each other or get married or anything like that, so don't ask.
How to end a relationship
To end your relationships, you have to send your friendship into a negative level. The only way to do this is to annoy your chosen character, through pushing them around, ignoring them, or using prank magic on them (flatulence, metal basin, lightning, sleep) enough times.
Doing this will make your chosen character revert back to an acquaintance, and thus you have to start from square one if you want to befriend them again.