You both have a case of the nerves and tension is thick. There are some simple ways that you can put your date at ease and lessen some of the anxiousness that she might be feeling.
The most important thing is to be conscious of, and not intrude, personal space. The majority of people have a "bubble" of space around them, usually 3 to 5 feet, that they do not want others in. Be respectful of this and don't force yourself past her comfort zone when the situation does not call for it. Obviously, dancing or sitting together in a movie theater are going to be exceptions.
Engaging in too much physical contact, too soon can result in your date wanting to escape as quickly as possible. Take things slow, watch her body language and follow the pace she has set. Everyone has their own individual preference as to what displays of affection are acceptable and how soon they can be shown.
Most people feel comfortable talking about themselves, their interests or things they know. One way to break the ice is to ask her a question about something that requires more than a simple yes or no response. Really listen to the answers given and when possible, toss out follow up questions. This will put her at ease, while giving you a chance to learn more about her.
At different times, inquire if she is comfortable. "Is it too cold in here, shall I turn the heat up?" Or "Do you like this music or prefer something else?" By letting her have some input on the date, she will begin to feel more at ease in your company, since you obviously care about her comfort.
Given a bit of effort, it usually is not too difficult to put your date at ease. Show respect of, concern for and an interest in her, and you will likely do well.