This is a tricky topic. Because self-awareness is a gift. I'm not exactly sure how much of it is natural, and how much can be learned, but we're going to try.
You know those people in your lives that can just ramble on about their boring stories without taking a breath?
Recently, one of these people in my own life was complaining about people who do that.....
It blew my mind. They totally understand the pain of being on the receiving end of a boring storyteller, but simply don't have the ability to understand when their own stories are boring.
Now, this is tricky, because our own lives are naturally interesting to us. But, if you have the ability to do it, think about whether your story would interest you if you weren't involved in it. And if not, don't tell it.
If you don't have this self-censorship ability, concentrate on brevity. Jump to the punchline as quickly as possible. Don't get hung up on details like...
"So last Monday...or was it Tuesday?....I can't remember if it was either Monday or Tuesday? But, whatever, anyway..."
Lose these lines in your storytelling. Stick to the point, get there and then give up the reins in the conversation to the other party.