For a guide to the federal executive-branch regulatory process and the process of conducting federal administrative law research in general, see the Law Library's Administrative Law Research Guide. Federal agencies' regulations appear in the following publications:
Both federal and state agencies will issue guidance documents to help apply and interpret education statutes and regulations. These documents in themselves can also become subject to court challenge.
For example, in 2016 the Department of Education issued a guidance document directing schools to allow transgender students to use bathrooms and locker rooms matching their gender identity. Many school districts and states challenged this guidance, both through legislation and litigation, notably in the case G.G. v. Gloucester County School Board, 822 F.3d 709 (4th Cir. 2016), which was appealed to the U.S. Supreme Court, but remanded and vacated after the Trump administration revoked the guidance document.
In the federal government, many of these guidance documents are available through the Department of Education website. To find guidance documents for a specific state, consult that state's administrative agency for education. In most states this will be called the "Department of Education," though the names vary.