What do I say to her?

It's less about what you say and more about how you say it. However it is good to get an idea of what you want to say and try to plan how the conversation will go. Maybe practice in the mirror. Relax, be yourself, pay attention to her and give relatable thoughtful responses.

As far as an opener, I recommend asking her hey are you [insert name]? I think we had X class together in high school. After she responds be sure to introduce yourself and maybe shake her hand if it feels right. If it is her, talk about the class and what you have done after school. If it's not her you could say "you reminded of someone" or if your feeling bold "you remind me of a girl I had a crush on back in high school". Keep the conversation going by asking casual questions. Try to keep her talking let it flow and keep it casual/low pressure. If you know you are going to see her again tell her "see you again later" at the end of the conversation. If you feel like you are going to be able to see her consistently, maybe keep talking with her and get familiar with one another over a few interactions to increase your chances. You don't even necessarily have to ask for her number or anything yet if you know you'll get to talk to her again in person.

After a few interactions and once you feel like you have established some mutual interest, say "so, [insert name] we should go out sometime". And then hope she says yes. If she does, then ask for her number. Be cool act confident and like you talk to people all the time. Be kind and relatable and don't come off as smug though. Have something planned ahead of time with a day and time and have alternative suggestions

If your having trouble finding the courage to talk to her, that is completely normal. That initial interaction is always the hardest part. A technique that helps me is to get naked and stand in the shower looking up at the nozzle. Stare at the nozzle and say "Hey [insert name]" then turn on the water as cold as it will go and say "we should go out sometime" no fear no hesitation don't think just do it. Just do it no matter the outcome. You will regret it if you don't.

I was in a situation very similar to yours. I followed all of that advice and when I did ask her out, she said she just wanted to be friends. However we met back up later and we are going out now. Having courage and taking initiative is very attractive and more rare these days. Go for it and be proud of yourself no matter what happens

 

Act as if she's an old friend that you haven't seen in a while.

Just say hey (name), we had this class together... be curious and interested about were she went after high school and what she does now.

Don't make a big deal about it.

 

@Abird

Hey bro,

Dont know how long you have been eyeballing this girl, (i think she knows) but the fact that she took a place closer to you might suggest that she's interested in you. Probably facing her own fears trying to talk to you.

That right there was your biggest shot but you decided to go anti social mode and put on some headphones.

Please promise me not to let an opportunity like that slip again.

As for talking to her...

Try asking about her study, if shes wearing headphones... ask her what music she likes. Find something you both enjoy and discuss that topic. Use what you see... tattoos have stories, in some cases do jewerly. Make a comment about her hair, all girls like that.

Make some jokes along the way, most of them are easy to pull off. Let your guard down. Be who you are, not who you want to be.

Trains stops??? You ask her number.
After that, 1 easy text should get you on a date. " Really had fun with you on our way home, next time coffee at my place? Maybe we can talk about (insert topic you both like) so more.

Sounds easy but it isnt i know.
Sometimes you just have to YOLO.
In case she says no, you can spend time on other girls.

Either way its better to talk to her, right?

W.I.P.

 

"Give a man a fish and you feed him for a day; Teach a man how to fish and you feed him for a life time"

With that said though, it's only valid for the second part of your post, the first part is solid dick.

Abird, it's best to know what you want and knowing you want to date her is half the job done. However.. don't let that hang in your mind or it will overcloud your judgement. Awkward silences arise from an unspoken train of thought / truth. When your mind tries to process "Hi how are you" + her reply and your "I want to date her, but how? holy shit i'm sweatingisshenoticing?" It tends to get overworked and scenarios like her saying "Dude, I know you, we had class together right?" and you replying "I'm good as well, thanks!" tend to happen.
If you think you're at a point where "wanting to date her", is pushing hard on your mind, then the best way to open up is.. with that.! That's the reality (I mean it as, that's the line to follow), you may think, or may have read that you have to x and y to please / talk to a woman, but the truth is, believe me, you just have to be you. If it doesn't work, it doesn't work, it's rather simple once you get it. I strongly advise against creating a persona which she "likes" only to ease her into who you really are afterwards. Think about it, you wouldn't want that happening to you either.
Back to how you open, I didn't mean it as coming straight out you want to date her, that's just a fantasy of yours that needs to be connected with reality and see if you're actually that interested (maybe she's into killing children, I mean, you can't judge just by her hips) so instead just be open about you being interested in her.
Also, practice something along with mirror talk, take deep breaths, calm your voice and relax yourself into the world. When you ask a question, wait for the answer otherwise don't ask. "Hi, how are you?" - wait, look around you, notice her, notice what she's doing. If you feel like smiling like an idiot, do it, because most likely you find her cute and want to rip clothes off and poney her into Valhalla, relax. You've had class together, you have a common "territory" but don't overuse it, it's nothing more than setting a familiar feeling; Again, don't forget to not beat around the bush, everyone senses that, it's what I first mentioned with "awkward silences". Be firm in what you want, take control of yourself.

Hope it helps!

 

If you know her and she has been sitting in the front and now has moved to the back were you sit its a good sign she wants you to talk to her. Go for it and don't overthink it she is moving toward you its a good sign

 

I still like @Mankrik 's advice. Start a conversation, ask questions with more than "yes" or "no" answers. Canadians have easy conversation starters because we usually apologise for something, then ask, "Hey, aren't you....?"