Make the conversation about them and shyt relevant to their interests.
How do you determine what their interests are? LISTEN AND OBSERVE.
No matter how shy a person is, they'll always drop little nuggets of personality into the conversation. Pay attention to what they say, how they dress, gestures they make. Make inferences. You see them wearing some logo on their t-shirt, hear them listening to some music, see them reading a particular book, engage them about it. Don't be aggressive -- just be friendly. Sooner or later they'll feel more comfortable around you.