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After you've hung out with the popular girl and her friends a few times at school, invite them to meet you somewhere public like the mall, the beach, or a coffee shop. A public meeting takes the pressure off everybody--you don't have to worry about how your house looks, and she doesn't have to feel awkward about going to a new person's house. Make the invitation as casual as possible. Try saying something like "I was going to go shopping for a homecoming dress Friday, do you guys want to meet up at the food court or something?" When you hang out with her outside school, pay attention to the cues she's giving. If she seems enthusiastic about hanging out with you, looks you in the eye, laughs, and talks about making future plans, you're well on your way to becoming good friends! If she spends all her time looking at her phone, shows up late, and barely talks to you, reconsider being her friend. If she doesn't seem like she had a good time, wait a little while before inviting her somewhere again. If she does mention future plans, don't be afraid to bring them up later! Say something like "Remember when we were at the boardwalk and you said we should all go to one of the outdoor concerts? There's a really cool one this weekend." If she invites you to do something with her, show up if you can! If you really can't go (for example, if you're grounded), be honest about why you can't. If you make up an excuse, she might think you don't actually want to hang out with her. After you've hung out for a few times, invite her to something a little more personal, like a party or a sleepover at your house. You can invite her group, your group, or a little of both. Try planning fun activities like manicures, watching funny movies, baking cookies, and makeovers. Keep the invitation casual. Don't beg her or guilt her into going. Just say something like "Hey, we're having a sleepover at my house this weekend, want to come? We're doing karaoke and makeovers."
Invite her to hang out in public. Listen to her cues. Show up when she invites you somewhere. Invite her to a party or sleepover.