Compiling legislative history, particularly on a federal law, is an exhaustive and exhausting process. Entire books have been written on the subject. I recommend that you start with -- or refresh your memory with -- a good online guide to federal legislative history. I think this one, from the University of Vermont Law School, is particularly good.
The resources listed in the box above also are good for legislative history materials.
If you are starting with a statute on Lexis or Westlaw, use the annotated code to review what materials may be available. The code editors put in a lot of work to find what legislative history materials are available for each statute. There is no need for you to repeat that work. Not all of the materials they cite to will be available on Lexis or Westlaw, particularly older materials. However, you can take that cite and look it up on ProQuest and usually find it there.
On Westlaw, once you have your statute pulled up, click the history tab and then review Bill Drafts and Legislative History Materials.
If you have found a citation to a legislative history document that is not available on Wexis or the free sites such as GovInfo or GovTrack, try using the ProQuest database. Once on ProQuest, use the "Legislative and Executive Publications" drop-down menu in the upper left to select Search by Citation.
Once on the Search by Number screen, use the menu on the left to select Publication Search, then Publication Number. This will allow you to retrieve just about any federal legislative history document with the citation.