Summarize this article:

Put a big smile on your face and walk over with confidence. Start the conversation with a warm hello and tell her your name. Try to avoid using any cheesy pick-up lines. She will probably see right through it and you may come across as disingenuous. Shake her hand too as a friendly gesture. Not only will she think you're a real gentleman, touching someone is a subtle way to flirt. If she's sitting alone or even with a friend, ask if you can hang with them for a bit. Don't just assume she's in the mood for company or a chit chat. Your politeness will work in your favor. Keep the subjects light, casual and fun. This should be a lighthearted exchange about very general topics. Consider, for example, asking her where she grew up, what school she attended, what type of music she listens to or where she's traveled to recently. Try to let her do most of the talking so you can really get to know her. If you are still stuck for conversation starters, consider that you clearly like the same types of places so ask if she's been there before or what her other favorite spots are around town. Let her know that you really like her eyes, her smile or her hair. Keep in mind that you don't have to compliment a physical attribute. Think about pointing out how great her sense of humor is or how smart she seems to be. It would be easy to overdo this but don't. One compliment will do. Keep it short and sweet. Just enough to let her know you find her attractive. This is your first interaction so it's completely acceptable if it only lasts a few minutes. Don't feel obligated to camp out for hours on end. Look for signs to see if she's interested. Things to look for include: smiling, touching her hair, making direct eye contact, asking follow-up questions or touching your arm. If she's not interested, she may have her arms crossed or be giving one word answers. Before leaving, ask if she might be interested in seeing you again. If you've been paying attention to her signals, you will know the answer to this question before even asking. Instead of getting her number, consider giving her yours.

Summary:
Introduce yourself. Ask to join her. Strike up a conversation. Pay her a compliment. Don't overstay your welcome. Make plans to meet again.