There are a few good print resources about preparing for case competitions.
Anderson, Chris. How to give a killer presentation. Harvard Business Review, 91(6): 121-125 (June 2013). Available in Business Source Elite.
Maister, David H. How to avoid getting lost in the numbers, HBS Case 9-682-010. Available for purchase from Harvard Business Publishing.
One important component of preparing for case competitions is the ability to apply theory to your case analysis. For example, you may be assigned a case about brining a new product to market. You could discuss the product development lifecycle as part of your analysis of the case.
The Value Based Management site below includes a synopsis of many common business and management theories that can be used as a starting point when doing a case analysis.