At any point in the story, jump sideways, and tell us more about a specific element. Then, jump back into the main story. 

Let's use the Three Little Pigs as an example. 

For instance, "The first little piggy built his house out of straw." Now, jump to the SIDE a little and tell us more about this piggy. 

Let me tell you a little bit about this piggy, He was the youngest of the clan, and he was not just lazy, he was REALLY lazy. There was the time when he was in school, and his teacher had given an assignment...etc

Here's another option:

Let me tell you some little known facts about straw. Straw is actually a very strong material, when used the correct way. In some cases, when straw is properly bound together, it can be impervious to all the elements of weather. If you travel to England, you will see hundreds of thatched roofs made out of straw. Not only are they sturdy and stand up to the harshest of elements, but they would probably stand up to the foul breath and huffing and puffing of the wolf! Not so with the way that this little pig built his house.

Now, jump back to the rest of the story. Later, make another jump sideways for a bit.

The second pig built his house with sticks. 
You may have already noticed that this little piggy was the MIDDLE child, and he was the CLASSIC middle child! He was always trying to do the right thing. He was also the buffer between his older and younger brother. They would always start fights, and he would always get in the middle. He was a bit clumsy, and would cry at the drop of a hat. He hated conflict, and would avoid it at any cost, thus the role of mediator!

Then back into the main storyline again. These little jumps to the side are great fillers where needed. Don't forget characters that may not actually be present in the storyline. The mother of the pigs...maybe even the mother of the wolf!

Use the setting and other, non-essential characters too: The town pigs, the straw seller, brick seller, etc. Let your imagination spread out and go wild.

You can always shorten the story to its bare bones, but having these little side stories can stretch it out and fill time when necessary.