If a guy stares and smiles at you in class but you actually don't know him pretty well does that mean he could possibly like you?

Well, if he knows you like him, then he may just be thinking if he likes you back, or if you just wish you never met. But if he stares at you, there is a possibility that he likes you too. If he continues to stare, maybe you should go up to him and ask why he stares at you. If he gets nervous and says he wasn't staring at you. Remind him that you like him, then ask him if he would like to go out with you. If he says no, don't rush, give him some time, and flirt a little, but if he says yes, do what you can to keep the relationship going.