What information should I research about a company before approaching them for sponsorship?

Research extensively before making contact: study the company's website for their initiatives and objectives, find bios of key people, reach out to others who have worked there, understand their products and how they're used, learn their brand values, and identify what problems they're trying to solve. There's nothing more impressive than when someone shows up knowing and understanding the brand instead of just asking for money. Google makes this research easier than ever - you can learn a lot about a company and its people before you ever speak to them.