How do I act like a girlfriend?

You act the same way you acted when you were single. Except for flirting with other men - off limits while you're in a relationship. But you're still the same person he asked out so he must like you for you. It's understandable that you're nervous but try not to change your behaviour to fit some mould you think is necessary. Just be you. It's what he liked about you in the first place.