The Senate: Overview
Article I, Section 3, Clause 2:
Immediately after they shall be assembled in Consequence of the first Election, they shall be divided as equally as may be into three classes. The Seats of the Senators of the first Class shall be vacated at the Expiration of the second Year, of the second Class at the Expiration of the fourth Year, and of the third Class at the Expiration of the sixth Year, so that one third may be chosen every second Year; and if Vacancies happen by Resignation or otherwise, during the Recess of the Legislature of any State, the Executive thereof may make temporary Appointments until the next Meeting of the Legislature, which shall then fill such Vacancies.
Clause 2 has been partially superseded by the Seventeenth Amendment.
The following state regulations pages link to this page.