Let me first start off by saying that starbursts are not necessarily good design elements. Some might consider them somewhat annoying. That doesn't mean that people will stop using them. Often, starbursts are used to highlight a price point or other important information. If you need to create one for a piece (or you're designing comic book sounds), then this tutorial is for you. :)
*This tutorial is for those who have a working knowledge of Illustrator.
1. Create a new document. Set your fill and stroke then create an ellipse with the Ellipse Tool.
2. More than four anchor points will be needed to create the shape, so go to Object > Path > Add Anchor Points. Do this two times.
3. Now, an effect needs to be added. Go to Effects > Distort and Transform > Pucker and Bloat. The Pucker effect will make spiky points, and the Bloat effect is more rounded. Drag the slider to the desired amount.
Optional: If you want an uneven starburst, you can do one of two things. (a) Select the starburst then go to Effect > Distort and Transform > Tweak. Make sure that Preview is checked. You can play around with this until you like the result. (b) For a more controlled look, click on the shape and use the Direct Selection Tool (white arrow) to select individual anchor points.
4. That's it! You can add text if you like.
The above images are examples of the two options for creating an uneven starburst.