The American Classical League (ACL) hosts a Latin and Greek teacher placement service https://www.aclclassics.org/pages/teaching-jobs which focuses on available jobs in K-12 schools, although there are also jobs listed at colleges and universities, as well as private tutoring opportunities and positions for administrators at classical schools.
Employers may list jobs at no charge by following the link. ACL members may list a resume on the site which employers can then search.
As of March 23, 2016, there were 81 jobs listed on the site. Many more job listings will be posted at the end of April and into May, when administrators make hiring decisions and retirements are announced. There are likely to be over 200 job listings by the end of May. Each listing shows the anticipated start date for the position as well as the date on which the listing was posted.
To find out about requirements for licensure or certification in specific states, see this page of the SCS web site or consult the site of the National Council of State Supervisors for Languages (NCSSFL). You can submit specific questions to the Supervisor for a specific state whose contact information can be found here.
For information about the ACL Placement Service, contact Cynthia White, Placement Director, at placement@aclclassics.org.