How to ask this girl on a date?

Ok so there is this girl that just moved from another school about 2 months ago. I only see her during lunch and I can tell she is very quiet, but very cute,which is exactly the kind of girl that I need considering I'm on the more quiet side as well. She sits with the same group of people and when I look over every now and then at her she'll hardly say anything and if she does it's too the person beside her. I follow her on Instagram and every time she post something she'll put #single or #hmu or something like that so I know she's kinda looking for a boyfriend. But that's not really the reason why I want to ask her out or at lest get to know her. I just know she's exactly my typpe and I need to say something to her. But I just don't know what. I've tried texting dm her on Instagram but the conversation was short and I didn't really get much out of it. Also this girl doesn't know who i am. So what would your suggestions be? Should I go up to her after lunch and say something to her? Should I start by saying just hi to her? Also I never see her in the hallways either. Just at lunch . I've also tried sitting with the same group she sits with but didn't really say anything to her cause I didn't want to put all the attention on her or anything. I told her she seems very quiet off a conversation we had a Instagram and she admitted too it, so I know she is. So what should I do?