ASTM is a nonprofit, non-governmental group that oversees the creation of internationally peer-reviewed guidelines for materials and safety. Asbestos falls under this purview and receives attention as a hazardous material. Since 1995 in the United States, such standards are required by law to be referred to if no preexisting governmentally-developed standards exist.
Two ASTM standards apply specifically to asbestos inspection and actually cross-reference each other. ASTM E2356 - 09 (Standard Practice for Comprehensive Building Asbestos Surveys) specifically deals with types of asbestos building inspections. ASTM E1368 - 05e1 (Standard Practice for Visual Inspection of Asbestos Abatement Projects) governs how inspection should proceed during asbestos removal from initial discovery through final site cleanup.
Training to ASTM standards is offered in a number of places, but none more convenient than the ASTM website. Comprehensive asbestos training is available on-site only and covers the standards listed above. This training goes further than U.S. federal standards mandate.