Autism Understanding and Training in School Methodologies for Educators Act of 2013 - Authorizes the Secretary of Education to carry out a demonstration program to award 5-year grants to eligible local education agencies for the following purposes in schools for children in grades pre-kindergarten through 12:

• providing training to teachers, paraprofessionals, and other staff on effective ways to teach, communicate, recognize, support, and interact with children with autism spectrum disorders in the classroom;
• providing technical assistance consisting of consultation on the type of training needed, hands-on opportunities to practice and perform newly acquired skills and methodologies, and post-training support to ensure accuracy of implementation in the classroom;
• executing strategies for recruiting and retaining skilled personnel participating in the education of children with such disorders; and
• implementing a program of parental support and involvement in the education of students with such disorders.