When a school wants to hire you, the process usually begins with an email. With successive emails, you and the host iron out the terms and details of your author visit.
While some authors then send a formal contract to the host to sign, I send a Letter of Agreement. This is essentially a contract in “normal speak” rather than “legalese language.” I also include a sample schedule and an author visit checklist to assist with planning. Here are the links:
Sample SCBWI Lecture Contract (SCBWI members only)
For more examples, type “author visit school contract” into a search engine. Also, I encourage you to check with colleagues to see what kind of agreement works best for them as you create (or update) your own.