When statutory language is ambiguous, sometimes courts look at the legislative history of an act to figure out Congress' legislative intent. What did Congress mean when it used a particular phrase in an act? Or more broadly, what was Congress' intent when it enacted a part of a statute?
Legislative History Example - Definition of the Phrase "Moral Turpitude"
"Moral turpitude was not defined anywhere in the INA, so attorneys and courts have looked to the legislative history of the INA to see what Congress meant when it used the phrase "moral turpitude." (Sadly, the legislative history provides no guidance.)
Legislative History Example - Was Eligibility for Asylum Required before Changed Circumstances
When Congress enacted language excusing late filed asylum claims due to changed circumstances, did Congress intend that an asylum seeker had to be eligible for asylum before the changed circumstances? (It depends on whether the Circuit Court of Appeals accepts the below argument about the legislative history.)
The easiest way to conduct legislative history research is to just search cases and secondary sources so you can find the info from someone else who has already conducted the research! After you find citations to legislative history documents such as the Congressional Record or House/Senate Reports, you can use something like Proquest Congressional to retrieve the documents to look at them.
Once you have found some citations to legislative history documents in secondary sources, you can use a source like Proquest Congressional (available through the Law Library's list of databases) to retrieve the documents.
You can click on Search by Number to retrieve documents using their citations.