I recently have dealt with this dilemma, but everything's going pretty well at the moment. I didn't think I'd be able to do it, too awkward, not normie enough. But I did it.
I went on a few dating sites and apps, messaged a few people. I had a bit of alcohol to loosen up, and I was able to hold a somewhat interesting conversation. Looked up things to talk about, and various videos on not being awkward.
Met in person, went on a date that wasn't face to face the whole time like dinner. Took her to an arcade. We clicked and it wasn't toooo bad or awkward, just talked about random topics, so I escalated it to diner. Again, we chatted a bit, then we sat in a park for 4 hours again chatting.
I was amazed how simple it was, most girls like it when you listen to them, their troubles stories and interact or ask questions when you find something interesting.
We've meet a couple more times, and have talked about a ton of stuff. Now she wants to be "official".
Surprising simple for all the overthinking I'd done and was so nervous about. I was upfront with my nervousness, but not to the point of being weird about it, I think she'd liked that, showed honestly.
Anyway, I don't know if I could go up to a stranger and ask for their number, but if you're able to listen and engage every once and a while about what they are talking about, and ask simple questions like "Do you have and pets?" which can lead onto talking about a variety of things depending on their response.
Steer away from SUPER cheesy openers, embracing cheese helped when used sparsely, just open with something you saw about them. It's quite easy with online dating since you can read their profile and see their pictures then bring up something you may have in common. Surprisingly, saying cheesy things actually engaged her and made her laugh, so using it tactfully can have a positive impact on how she views you.
If you're too nervous or shy to try in person (like me), try some apps and dating sites.