Set the Tone
When you first meet, set the "boyfriend/girlfriend" tone right away. Be clear in your actions and words that you would like to date the girl, not just be her friend. You don't need to explicitly state your intentions, but be clear if you are asking her on a date. Flirting with her is a good signal that you aren't trying to become her friend. Also, set the tone that you aren't just looking for a one-night stand.
The main difference between a player and a boyfriend is how quickly he wants to rush into a sexual relationship. Players will want sex early on and some girls will be suspicious that these guys won't stick around after. Guys that take their time are usually interested in a relationship. While you don't need to be chaste, follow her lead on how quickly she wants things to progress.
A woman wants a man who is respectful to her. If you want her to be your girlfriend, you have to show her that you are worth the commitment. Be respectful in words and actions. Respect her time by not canceling at the last minute or expecting her to wait for you to call. Always be respectful of her ideas and opinions, and she should reciprocate. If she feels disrespected, she will not want to be your girlfriend.
Don't fall into the "yes dear" listening mode where you only partly listen when she speaks. Being a boyfriend means building a relationship. Getting to know her means really listening to what she says and asking follow-up questions. If she feels heard, she will trust you more and want to be your girlfriend.