How do I get better at telling stories about myself?

I feel like I have a lot of great stories and experiences, but struggle to share them socially in a way that's not awkward or non engaging.

It's like I'm sharing it as an independent anecdote than having a conversation. How do I tell stories and let the other person feel more engaged and interested and part of the conversation?

I especially mean this in the context of dates or even just new friends.