as in, someone who you only started talking to recently but feel like you connect with ok!! I feel like I'm overthinking how awkward this question is?
I tend to overthink things, too. Maybe just try something simple, like "could I have your phone number?" Or you could ask them if there's another way you could keep in touch outside of whatever it is you know them from.
I find myself overthinking these things too, definitely. So personally I would first ask for it in a casual, platonic way, just as friends. Then, you can maybe tell them eventually or soon, whatever you want, that you like them romantically. TIP: I've used one thing before that helps me once you DO have their number and you're texting. I'll bring up something about crushes and wait for them to ask me if I have a crush. Once they ask, you send, "yeah, you" and wait for a response. Of the response is negative, you correct yourself to "yeah, you?" This way it won't be awkward for either of you because your crush on them is still hidden. I don't know if anyone else likes this idea, I do though. Hope this helps! Xoxo Artist Girl
Just ask for the number, without fanfare or evasion or a complex prelude. People know when you overthink things. When you learn to start being direct, the next time becomes just a little bit easier. If a friend is going to give you their number, they will give you their number.
I'm with silverhalo, I always give my phone number first and it's quite logical that they respond with their own number. Don't overthink, it is a very simple act and a natural part of forming a relationship. Just say that it is easier for you to keep in touch via phone because you're not often in facebook or something like that.