I'm the same way. I just don't like talking to new people. What I try to do when someone asks me a questions is reply with a yes/no/one-word-answer like I usually would and then add an extra piece of information or ask a question. That's how I try to keep the conversation going. If you add extra information, they could ask you about that or maybe make a comment and a conversation could develop from there, or if you ask a question, they can reply and they'll leave the conversation feeling like you're interested in them.
In class, try talking to the person/people next to you. It can just be small things, like 'can I borrow your ruler?' or 'what did you get for this question?'. Usually those conversations only last a few seconds - question, answer, thanks - but it shows people that you're social and open to talking. Also, the longer you leave it, the more awkward it becomes. Sitting next to someone who you never talk to? SO awkward... Just having a friendly relationship with the people who sit next to you (even if you don't talk to each other at break or outside of school) just makes your day so much easier. They might start to talk to you, too, and you could soon find yourself chatting about other stuff and becoming friends. If not, that's okay too - you can just look at it as practice :)
Good luck :)