There's a fine line between being complimentary and being a suck-up. But, if you've read "Does brownnosing really pay off?," you know that compliments can work to help get in someone's good graces -- as long as you aren't too obvious about it.
The key to sounding sincere is to be sincere -- if possible. Find things that you honestly like or admire about the parents. Mention how beautiful their house is, how wonderful the mother's meal tastes, how impressive the father's big-screen TV is. But avoid cheesy, overdone lines, like telling her mom, "You look like you could be her sister!" Even if you don't like something, you can skirt around a compliment without making one. For example, say with a smile, "This is an interesting dish. How do you make the meat so tender?"
Experts agree that you'll need to respect the house rules. If you're staying overnight, and they put you in separate rooms, obey their wishes.
Parents pay close attention to how a new beau treats their beloved princess. One of the best ways to prove your good intentions is to treat your girlfriend will all the respect and attention they know she deserves. Offer to take her coat, carry something for her or refill her glass.
But don't go so far as to show unseemly public displays of affection (or PDA). Anything more than holding hands or a peck on the cheek will probably make the parents uncomfortable and suspicious of you.