Practice.

Practice on yourself, out loud if possible, but in your head if need be.

Practice on friends and family is much better. You'll bomb and fail a great deal at first, so be humble.

Practice the same story over and over again. Tweak it, change wording and timing and the order of events. Try telling it in third and first person.

It doesn't need to be real or even make sense: "Once there was a homeless man who had a pink bazooka..." Then what? There are an infinite number of possible thens at any given point in a story; being a good story teller is about doing things unexpected with the threads you have already given your audience. It's about holding back the right amount, going for it when need be, and showing and telling in the right proportion.

A couple of good pointers is if you're completely stuck, state something obvious. "The sky was blue;" is better than dead air. And be sure to make things happen. A story all about moods and internal states is MUCH harder to make work.

As a starting point, take one of your short personal anecdotes and tell the story of what you wished had happened or what might have happened. Another good launching point is one of those short story generators online. Just do it all out loud or in your head; being able to write a good story does not always translate to being to tell one.

If you have trouble doing things to reduce your inhibitions can be very helpful. On that subject, sit at the bar and start swapping stories with strangers. You'll bomb some of the time, but some of the best storytellers I've met have been random people in bars.