There are many different types of materials involved in a legislative history. These include bill versions, committee hearings, committee reports, and congressional debates. To understand this process, and to be able to identify the documents you care about, take a look at a resource that explains the different types of materials. There is no dearth of such resources, but here are two:
One of the best pieces of advice we can give you when researching legislative history: Locate a guide/webpage/sourcebook that provides titles and links to reliable resources. One fast way to do this:
Google [state/federal] legislative history legal research guide
Here are some guides regarding federal legislative history that we like (by no means a comprehensive list):
Also, be sure to check out the Statutory Research page, for links to resources that provide background information and analysis about specific acts.
Often, the most efficient way to locate state legislative history material is to Google to locate a state-specific legal research guide. You might also check out your Bluebook: it provides the names of session laws and statutory compilations for each state in T1.
Many times state legislative materials are not as robust or as available. If they are provided online, it is frequently through the state law library, or state legislature. You may have to get more creative!
However, Lexis and Westlaw and Bloomberg do provide some materials:
Lexis and Westlaw and Bloomberg also provide legislative tracking tools.