You might say something as simple as “Hi, my name is Michael. I see you at the library every day, what are you studying?” or “You gave a great presentation! What inspired you to research that topic? My name is Sarah, by the way. ”
Ask questions that start with “how” or “why” to elicit more detailed responses. Take note of her interests so that, if you get to the point of dating, you can arrange dates that are exciting for her.
One way to talk to the girl you like about common interests is to say: “I loved Finding Dory too! It was so fun to see all the characters again. What was your favorite part of the movie?” If you go to the same school, you might even ask her for help with a homework problem. This will give you an opportunity to spend more time together.
Be careful not to overdo it by going wherever she goes. All you need to do to create a sense of familiarity is pick a few strategic moments every week to be near her and make your presence known.
If you’re in school, this may mean talking to her by her locker or as she’s walking to her car.
Don’t aim for date-like situations. All you want to do for now is find opportunities to allow you to get to know each other. Dating, for a shy girl, may be a concept that she needs to warm up to, and warming up includes getting to know the person she might go on a date with.
Refrain from crossing your arms. If she’s paying close attention to your movements, she could mistake this as you showing a lack of interest.
If you said hi to her yesterday, say hi to her today. If you smiled at her when you crossed paths in the cafeteria, smile at her again so that she doesn’t think you were just being polite. Try to make eye contact multiple times. She will get your hints if you repeat them a few times.
Set an amount of time you’re willing to try to break the ice. For example, tell yourself that if after two months of you flirting with her you are still not spending more time with each other, you will either move on or try a more direct flirting technique. If she does make it clear she’s not interested, do respect her wishes.
If she doesn’t like you, you will see her become uncomfortable with your gestures. Her body language will be closed, she might not make eye contact, and she might be even quieter than usual.