1
Consider making the first move. No, it's the 21st century, but in general, men are still expected to approach women first. Of course, some women are more bold and proactive than others, so she might surprise you by asking you out first.
2
Be confident, and have a sense of humor. Women appreciate these qualities, especially when it comes to finding a boyfriend or spouse. This doesn't mean you should try to be somebody you are not, but make an effort to highlight these characteristics when trying to impress a woman.
3
Don't compare her to other women. Women tend to compare themselves to other women too often, and usually at their own expense. Many women feel dissatisfied with their appearances as a result. They may wear makeup when going for a walk or shopping at the supermarket, just because they need it in order to feel presentable.
If she's down about herself, it may help to remind her of her intrinsic worth, or about the way you see her.
4
Figure out what she loves. Does she like hugs, or verbal compliments? What makes her feel loved? This can help you display your affection in ways you know she'll appreciate most.
5
Be courteous without being condescending. Even a die-hard feminist will appreciate it if you hold the door open for her or offer to pay for dinner. Though she might not let you pay, the gesture will still be appreciated.
The line between politeness and benevolent sexism is whether you treat her like she can't do it herself. For example, it isn't condescending if you open a car door because you want her to feel like a princess, not because you think she can't do it herself.
6
Compliment her. Every woman likes to be reminded of how beautiful, smart, and sweet she is every once in a while. This is especially true for a romantic partner, who needs evidence that you are interested in her. Remind her what you love about her.