When do the requirements for State and local governments become effective?

In general, they became effective on January 26, 1992.  Revised regulations published by the U.S. Department of Justice on September 15, 2010 covering state and local governments, became effective on March 15, 2011.

For additional information, take a look at the following resources:

What is the Americans with Disabilities Act (ADA)? 

Timeline of the Americans with Disabilities Act