The Chronicle states that research statements are usually one to two pages long, but some might be up to seven pages long. A hiring committee will be reading your statement among many, so it's a good idea to make it as concise as possible. Stanford University recommends five paragraphs as a starting point.
Include your research accomplishments and goals. Write why you will be a successful addition to the department and why your research is important. Include what gives you an edge over competing candidates. Stanford University suggests using a basic formula of "Big Problem + Challenge + Approach" to explain what and how you research.
Remember the type of school, department, and position involved, and adjust your writing accordingly. Include why you and your research are a perfect fit for the job. The University of California San Francisco suggests being personal by using "I" and "me" and shying away from too-detailed writing. Be passionate.