In almost all general, 4-skills ESL textbooks such as Smart Choice or World Link , there are usually pages with discussion starters that involve telling a story of some kind, often in the unit related to the past verb tenses. A big problem with telling stories in class is that most students will not do a very good job of it if they are given no time to prepare. And an activity that could be very useful for generating some interesting conversation and discussion can be over in only a couple of minutes.
A better way is to give the students 2-5 minutes (depending on the level) of preparation time before they have to tell their story. I emphasize to the students that it is a speaking activity and not a writing activity, so while they can jot down a few words, they cannot write full sentences.
Once the time is up, you have a few options. If you have a small class, you can listen to everyone’s stories. Or, put the students in groups of 3 or 4. Each person goes in turn telling their story and every other person listening will have to ask them 1 question. Emphasize that everyone is to listen carefully to the story and think of 1 interesting question to ask the student and not just to think about their own story. You can review the “W” questions for low level students, if required (who, what, when, why, where and how) and also give some examples of good and bad questions.