As someone who transitioned from a deeply introverted anxious young adult with a persistent stammer, to a relatively outgoing person who is capable of clear communication, the secret is caring less and forgetting that you exist.

There are steps though to get there:

• Look at a person. De-age them back to when they were a shy or excited or inquisite toddler. That's their base model. Anything built on that is just extra wisdom or fluff or bluster.
• Talk to people like you would an innocent child, just use more grownup words.
• Cheat questions:
  • "How was your day today" "what did you get up to" "hows your upcoming week looking"
• Cheat responses:
  • "nice!" "well done!" "oh damn"
• Cheat moves:
  • Eye contact. Look at people in the eye, then look away when describing something, then look them in the eye again.
  • Nodding: Make nodding gestures as they respond to you
  • Hands: Gesture with your hands when you describe something.
  • Smile: You don't need to smile, but it helps. You can look away when you do it.
• Listening helps but is top-tier and isn't a requirement
• Learn to build connections through topics though. If they're talking about cats, remember your dog.
• Signal it's your turn: I suck at this and wait for gaps, which usually means I forget what I wanted to say, but you can signal in other ways
  • Yes: Finger gun and a nod whilst inhaling
  • No: Polite laugh and a head shake whilst exhaling
  • Random: if someone won't stop, they need to be stopped. Just jump in with your crab story, who cares.

This should hopefully get you along the way to forgetting that you exist in a conversation, and it should become second nature after a while.