On-the-Job Training Act of 2010 - Amends the Workforce Investment Act of 1998 to authorize the Secretary of Labor to: (1) make discretionary grants to local areas for adult on-the-job training or dislocated worker on-the-job training; and (2) use up to 10% of funds authorized under this Act to make grants to states, local boards, and federally recognized tribal organizations for developing on-the-job training programs.