There are some characters you can't date right now, like professors or campus staff. But if it isn't someone with a special role then you can usually approach them to talk by clicking the People tab, then click their profile, then select "Talk to him/her/them". There you can plan hangouts or dates with them. You can also plan hangouts and dates over the phone if you have their phone number.
Go on lots of dates with the person you want to date and get their Friendship, Lust, and Romance bars really high, then approach them in the evening to talk again. Eventually there should be an option to propose a relationship, though it can take a while. Like a month or 2 of ingame dating. Or if they like you enough they may beat you to it and ask you out!