How do I ask for someone's phone number without seeming pushy?

The main thing is not to rush it and don't push. If you've just met, just suggest exchanging contacts naturally, like it's the most obvious thing: "Let me give you my number, I enjoyed talking to you" or "Want to exchange numbers?" The tone is what matters - calm, no pressure. If they agree - great, if not - don't dwell on it. Don't ask for their number multiple times and don't keep bringing it up.

It's best to offer your number first. It shows confidence and takes away the feeling that they're being trapped. After that it's totally fine to say something like "How about you give me yours?" If they're actually interested in you, they'll reciprocate. If they refuse or hesitate for too long - accept it calmly. Pushiness starts exactly when people don't respect other people's boundaries.

All in all, it's simple: be straightforward but polite, don't drop hints and don't expect miracles. In my 23 years of experience I've learned that honest and open relationships are always easier than all these games. Same thing here - either someone's ready to communicate or they're not.