After that, just follow the next steps:
1. You can bump accidentally with that person and say something like this "Oh sorry! are you new? My name is...." that kind of stuff can work. You could also try asking their favorite hobbies and then sharing a little about yourself, not too much, just something casual.
2. After that the best thing you can do is seeing how she develops in the clasroom, i mean, you won't want taking this part to literally because you..... are going to look like a stalker, and that's not a good thing, besides, you might want to keep your distance a little bit, but still interested in knowing her/him better. If you notice that she/he's a troublemaker i recommend not to get involve, becauseat at first that probably look fun, but at the end the only thing that's going to do is get you in troubles. On the other hand, if you notice she/he's kind of cool but also responsable, go for it, it might be the cause to a good friendship consequence.