Meeting your girlfriend's -- or potential girlfriend's -- parents for the first time can be intimidating, especially if she appears to be particularly close to her father. Remember that a daughter is often the apple of her father's eye, and you may look like an imposing threat to a very special relationship. Projecting maturity, integrity and respect will get you very far.
Bring a gift. If you are being invited over for a meal, it is appropriate to bring something, whether it's a bottle of wine, a fruit basket, a homemade dessert or a wedge of gourmet cheese. Ask your girlfriend ahead of time what her father would most appreciate. Maybe he has a favorite beer; bring a six-pack. Her father will appreciate that you've put in the effort to research his tastes beforehand. Of course, if you are under 21, a gift of alcohol would be inappropriate.
Look respectable. You don't have to wear a three-piece suit or something that is otherwise seriously out of character for you, but remember that you are not going to baseball practice or to a video game convention. Avoid the standard frat boy uniform of jeans, T-shirt and hoodie, as you want to project an air of maturity. A collared shirt and khaki pants with dress shoes will make you appear more refined. However, comfort is also paramount. Don't wear fabrics that are itchy or clothing that is too restrictive, or you run the risk of appearing nervous by fidgeting and adjusting your clothing.
Be yourself. As cliche as it may sound, your girlfriend's dad wants to meet you, not some contrived image that you think will win you the most points. Remember that he was a lad once too, and he will likely be able to sniff out any dishonesty or exaggeration. While you certainly don't want to be deliberately rude or crass in an attempt to prove your individuality, you will show that you are a man of character by not compromising your values or your integrity.
Be honest. If he asks you a question, answer honestly. Honesty is a sign of integrity and the mark of true character. While he may not necessarily like your answer, he will appreciate that you were honest and not just saying what he wants to hear. You're not a fan of his favorite sports team? He'll get over it. What matters is that you stand behind your convictions.
Be interested in him. While the focus will likely be on you most of the time, don't just give your answers and then wait for the next question as though you're at a job interview. Keep the conversation flowing naturally by also asking him things about himself. For example, "Jill tells me you do graphic design. Can I see some of your work?" or "Did you really design this kitchen yourself? What was that process like?" For one thing, it takes the focus off you. Secondly, it gives him the chance to talk about himself, which most people enjoy.
Respect the daughter. More than anything else, your girlfriend's father wants to know how you will treat his precious offspring. Show him what a gentleman you are by looking her in the eyes when you speak to her, not interrupting her when she's talking, using polite language when addressing her and not making any kind of suggestive physical contact. For example, slinging your arm around her neck might show the father that you want to possess her more than honor her.
Use polite language. You're not at a baseball game or out with your buddies. Using vulgarity is a show of disrespect in the presence of elders. In addition to not cursing, you want to use language that reflects a gentile background. Words like "please," "thank you," and "you're welcome" will go a long way. Other ways to demonstrate politeness would be to offer to help set the table or wash dishes if you are joining the family for a meal. Offering to help out in any way you can will show that you are both handy and eager to please.