Use different voices for each character. For example, if you're telling 'The Three Little Pigs', make a high - pitched voice for the pigs and a deep, growly voice for the wolf. This will bring the story to life for the kids.
You can change the ending of the story sometimes. Instead of the traditional ending of 'The Tortoise and the Hare', you could say that after the hare learned his lesson, he and the tortoise became friends and had races together for fun. You can also incorporate the child's name or things they like into the story. If the child loves dinosaurs and you're telling 'The Little Red Hen', you could say that the little red hen's neighbor was a friendly dinosaur that helped her with the work.
Add some actions. While telling a story like 'Peter Pan', you can pretend to fly around the room when you talk about Peter Pan flying. You can also use props. If it's a story about a princess, you can get a little tiara and put it on the child's head when the princess is mentioned. Another way is to ask the child questions during the story. For instance, in 'Alice in Wonderland', you can ask what the child would do if they were Alice in a strange place like Wonderland.