As someone that is super introverted:
Just be friendly and easygoing. If you act nervous, generally it'll make me really uncomfortable around you and I'll be suspicious of you. If its someone you see everyday, maybe warm them up to you by throwing out a compliment and then leaving. Like 'I like your shoes.' Then smile and keep walking. I like this a lot, because it makes interacting with someone in the future a lot easier and makes me feel like it will be easy to end a conversation if I start feeling weird.
I really like getting written communication! That way I can process what you're saying without feeling rushed and can take my time replying without feeling like someone is analyzing everything I'm doing. I'm also way less likely to say no to suggestions of hanging out. This also applies to texts, IM, Facebook, email, etc. Also, if you're suggesting something like going out, try to set an end time (say you have to be somewhere or whatever) so that we aren't overwhelmed and don't get tired of being around people and act funny/bail.
Another great way to start a conversation with me at least is to ask questions that provoke my opinion. Like asking what I think about something another person did (or why they did it) will get a lot of words out of me. If its a topic I know anything about it will really light me up. Sharing personal information (but not TMI's) is a great way to get me to open up about my own, too. Hope that helps.