Just because a guy is a little quiet or shy doesn't necessarily mean that he isn't into you or doesn't want to make a move. Maybe he doesn't have much dating experience, maybe he just got out of a messy break-up and is a bit timid, or maybe he just has a shy personality. Don't worry---most guys will eventually open up and make a move if you give them the time and help make the situation more comfortable for both of you.
Find out what he likes to do, what movies he likes, what he reads, who his friends and family are. Having him open up and talk about himself will make him feel that you care and that you can be trusted.
Tell him about you, even if he doesn't ask. Let him know what you do for a living, what kind of hobbies and interests you have, who your friends and family are. This will give him the opportunity to respond, ask questions and be more comfortable with you.
Smile and be friendly around him. Always be yourself, but create a positive atmosphere when he is around you. That positive energy will be felt by him and he'll be more willing to get closer to you.
Let him touch you. Once he begins to feel comfortable with you he may try some introductory steps to making the move, such as holding your hand or giving you a hug. Because he is shy, this physical contact may be quite difficult for him, so don't push him away.
Flirt with him. Tell him how cute he is or how strong he his. Guys like to know they're attractive, and they will respond to your advances.
Make the move yourself. If you've done everything you can, try making the move yourself. Perhaps it's not that he doesn't like you. He might be inexperienced and oblivious to your signs of attraction. Some guys like a girl who knows what she wants, and you may find that he responds when you make the move.