Do you happen to have any favourite active players? It's definitely becoming more fashionable to follow players rather than teams these days, though many of us do still prefer the old school approach of having "our team". Still, if you've got a favourite player that stands out above the rest, you might find that you become a fan of their team by osmosis, so to speak.
Otherwise, is there a team that you particularly enjoy watching? They might be already on the way to becoming your favourite team! Doesn't matter if they're successful or not. Everyone has to jump on the bandwagon at some point. It's the people who constantly switch allegiances to the latest champion and pretend they're life-long supporters of them that draws the ire of their fellow fans.