The basics. You will need to understand the basic information about the company. This includes their contact information, structure, location, what product or service they are selling, financial profile, etc. This information is usually apparent after perusing their brochures, sales letters, web site, etc.
Understand their market. It also pays to understand who they consider their direct competitors to be. Do they perceive their market to be the same as yours? Do you share some of the same customers?
Any new products? If you can gain insight into anything new they may be developing, you can use this information to your advantage. Can you develop something similar?
How much of a threat? Assess how much of a threat the company really is to you. If they play a minor role in your competition, you probably won’t want to spend a lot of time profiling them.
Dig deeper. However, if they are a large competitor, find out as much information as you can about them. This includes any information on product development, suppliers, training methods, etc. The more you understand about their very infrastructure, the more you can apply this knowledge to your benefit.