The legislative process for state governments is much the same as for the federal government. Follow the same steps you would as for a federal problem:
Each state has its own resources for legislative history research. The availability and types of legislative history documents produced by state legislatures will vary considerably between different states. Additionally, the nature of the documents produced could be very different, for example committee reports at the federal level are quite detailed while some state committee reports consist simply of "pass" or "do not pass".
Usually, the best place to start state legislative history research will be the state legislature's website.
Congress.gov has created this page with links to each state legislature's website.