Humm… How far do you want to go? western school drama or japanese school drama? For japanese, I’d do something with the clubs… you know, COMPETITIONS, how hard everyone is working to be the best they can in tennis/swim/polo/racing/war-gaming/chess/whatever. While it would be tempting to have the group all be members in 1 or 2 clubs (so you don’t waste too much time on “solo” or “duel”), by spreading them out, you can establish the rivalries — rivals for the top spots in the club (how about a CHALLENGE for who gets to be the top diver— with a cliff diving contest witnessed by not only the diving club, but all their friends and siblings and what-not (you know, effectively “the school” or at least "the cool part of school:)— and rivals for love. You know, basic school stuff. Or you could have the president of the class die (accident, sudden biological death, whatever), and one of the players gets selected as the new president or bumped up to the assistant, and gets all the crap that goes with it (having to organize events, chores, whatever).
And you have work after school… since some of the characters may have an after-school/part-time job. You can have all sorts of ordinary “drama” there— like one or two of their co-workers is keeping a small litter of kittens in a back room, nursing them to be big enough to give away, after finding them drowning in a bag down by the river. They can’t take the kittens home because their SO, room-mate, or parents hate cats or are allergic— does the player turn them in or help them? Or, a hot boy/gal comes in and flirts with them a bit, they finish their business in the store, and leave. But from then one, a gang of “scary” people start bothering them and telling them to stay away from the hottie. Of course, small world drama— they keep bumping into each other (you pick— innocent or on purpose). Things start escalating.
And that’s not even getting into home life drama. You can make it the ordinary stuff of sibling rivalry (like— each one races to finish their homework, as the first one done gets to take a nice long bath, but the other will have to take a short one to get to bed on time for going to school the next day— would work best between brother/sister) to full blown Jerry Springer.
And if you want to really have some fun— player is going home, sees someone they want to avoid (there’s plenty in the above) and steps off their normal path into an alley and finds some business men wearing shades beating the snot out of another, older salary man. Something about the men just screams “yakuza” to the player, or perhaps he knows they one of them is because he recognizes the guy that picks up the protection money from the player’s part-time work. Whatever. Not wanting trouble, the player leaves it alone and pretends he doesn’t see anything— he just scrapes at the bottom of his shoe like he might have stepped into something unpleasant— and leaves. Later on, the player gets asked down to the local precinct, and a detective there starts hassling him about “I know you saw what went down. We’ve got you walking in and out of the alley from the ATM camera across the street. Now, just sign this to say what you saw.” A student would NEVER go against such badasses, (unless, you know, they are wacko to begin with), so they don’t go along, and the detective starts hassling them, pointing out how good citizens rat out the bad guys, courage, honor, you know, throwing the kitchen sink. Plus, people at school start thinking the detective thinks the character has done something bad, and things go downhill from there… for a while, anyways.
Seriously, life’s trivalities is easy to come up with. But how to make it IMPORTANT to your players, that isn’t. You might need to know them pretty well, so you can hook them with set ups that interest them.