Women will pay increased attention to those men who explicitly show they are interested in what women say or do. 
In other words, when your date starts talking, you need to show her you are truly fascinated with what she says and are also able to provide feedback. Just sitting near her and looking absorbed with her conversation topics bears no significance; she can easily assume you are faking your interest as long as you have nothing to say. In order to counteract such assumptions, you will have to work on becoming a good listener. A good listener is one who understands what the other talks about and proves he understands by always having an adequate reply at hand.
It is not extremely difficult to improve your listening skills. Just focus on her conversation preferences: most of the times, especially to what concerns first dates, women will talk about what they like or what they don’t like. Basic reactions like: “Why? Oh, and you know, I can perfectly understand that, I myself have a preference for…” or like “And when do you plan to…?” or “How do you plan to…?” are the first signs you are concerned with her concerns.
Also, stay away from placing the conversation under your complete control. You will most likely end up talking about you and your interests exclusively, while neglecting her. Women are great listeners, but they are also great talkers and neglecting this latter aspect of their “constitution” is an unconceivable manifestation of indecorum. In other words, you will turn in her Knight in Shiny Armor if, at the moment you are taking her on your white horse, you ask her how she should like to sit on the horse’s back, how she spent their day or where she wants you to take her next. Going beyond metaphorical aspects, a man couldn’t find a manner of approach more enchanting than truly engaging in conversation and making his enthusiasm visible.
