While I'm happy to see similar opinions, I will still summarize my own:
If you haven't been introduced to a person yet, you really shouldn't be romantically interested and attempt to get to know the person with that already in the background (Trust me, it won't end well. Personal experience).
Your question might be better rephrased as: How does someone like you with limited experience in dealing with girls introduce himself to new girls? (with possible consequences of romantic interest growing always being a possibility). Easy. The same way you would introduce yourself and start to get to know guys (I'm assuming you have some friends, and that they are male). Treat women like you would treat any other human being, don't psychologically prepare yourself as if you're about to try to interact with a new species (Because you're not.).
Make sure to introduce yourself and maintain the friendships of as many ppl as possible, girls and guys alike. Eventually you'll realize that you're romantically interested in one of those female friends, and by then, hopefully, you'll be comfortable enough with each other to discuss it, and both mature enough to accept whatever outcome comes out of such a discussion without having to make too much "drama" out of it (Basically, always be ready with a plan B, if she's not interested. You don't want to lose a friendship over something like that).