What are some tips for making a girl feel more comfortable around me?

If you're on a first date with someone, what I like to do is take the lead conversationally. Always be open to what she has to say, but take the lead until she's comfortable. Ask her leading questions about herself. Also, be open to talking about yourself. By doing that, you are showcasing yourself, your personality, your beliefs, desires, and values. People then tend to follow suit, especially if they're shy, They'll take your lead. Physically, you're looking at her comfort level when it comes to both emotional comfort as well as physical comfort and you're taking the lead from how positively she's responding to both.