Would this be awkward to ask?

Okay, so I've been friends with this girl for awhile, and I had plans of asking her out, but I waited way too long. She gave me the right away and has been giving me extra atention for awhile since we started talking. I don't know why I didn't just go for it; and recently she started seeing someone else, who I know but am not really friends with. I don't really know what she sees in him but that's not really my businiess.

I never got her number as it never came up and I never asked for it or asked her out. I still wanna get to know her more as a friend or eventually more, but would say asking her to hang out or asking her for her number at this point be awkward/look like I was looking for more than friendship, and if not what should I say :x. I'm bad at this stuff. :(

Just causually ask her what he plans are for one weekend. Then suggest to meet up. This is how friendships start! You said she hasn't been dating this new guy for too long, so who knows if they are serious. It doesn't hurt to have another friend anyhow!!
keep us posted!

Ya, I was thinking that, but I just don't want it to seem like more if she doesn't want it to be. That's if I can even talk to her alone.

Okay well, the last few days I haven't been able to catch her alone, and it would seem she's been avoiding eye contact and no special treatment, no smiles, nothing. So I'm gonna guess there's no chance at this point.

...but, I'm having another problem. How should I approach a somewhat random person I don't know and ask them out? Is that bad in high school?

Generally, you have a conversation or two before asking someone out. Based upon those conversations, you can usually get an idea if someone is open to you or not.