"I'm interested in you and would like an opportunity to get to know you better."
That's your approach. Simple, honest, authentic, respectful. But you've gotta do it. As UCLA basketball coach once said: "You miss 100% of the shots you don't take."
Request for the men: Read the room. If a woman isn't interested, you'll know immediately. Move on.
Request for the women: Please understand the dating climate we're in and meet men halfway. Smile. Make eye contact. Give them some credit for trying, and if you're not interested, at least be gracious.
This isn't rocket science, people. It's dating, and with a little finesse on both sides, you might just be able to actually enjoy it.