It doesn't even have to be a story; it could be any introduction related to the trick. A quick piece of advice is to watch some magicians perform, and learn from their performances. Some good magicians that I think perform well are Jay Sankey, Penn & Teller, Kostya Kimlat, Paul Gertner, Shawn Farquhar, Michael Ammar and Lennart Green. All of the mentioned magicians do close up (although Penn & Teller do mainly do stage) since I discern that you perform to your friends and family. Also, if you watch some of the shows of the mentioned magicians, you'll see that some don't even give an introduction sometimes, but their presentation is still pleasing. That's because it's not just about introduction, it's about keeping that presentation along with the trick. You don't tell the story and then do the trick; you tell the story as you do the trick.