Key things to keep in mind:
Use your body as a communication tool
We're physical creatures and if you want to get her interested in you sexually, you sure as hell aren't going to charm her into bed with only wit. Use light taps on the shoulder when emphasizing points, give her hugs, keep strong eye contact when talking to her.
Don't be an emotional tampon
Girls are really talkative while guys bond through doing activities. Know how you get classified as just another friend for the girl? You're always there to listen to her emotions. It's good to care about people but you need to show her that you're a man who's interested in her. Not doing so is an easy way of getting friend zoned.
Don't be a white knight at her service
If you comply to her every request, you seem overeager to please her and win her attention. She's going to be thinking, I guess people don't really like him since he's bending over for me.
Be confident and learn how to lead
Take charge of situations and act like you do. People like to be inspired and to follow people who have natural charisma. If you ask her for her number, do so in a confident tone and not like a meek little bitch. If you want to take her out on a date, say at x time we're going to blah blah blah. Don't ask.
You're the prize to be won
Sure you're interested in her. But she should qualify herself to you. You're a great catch. What makes her so special compared to all the other girls out there? By keeping this mindset, you remain confident and you don't put her on a pedestal. Tangentially, live an interesting lifestyle. No one wants a guy who simply plays video games. It's fine to have an interest in it (hey, I play it too) but have other motivations out there in life. Pick up a sport, read some books, go work out, have a plan in life.
That's all for now.