Debates on the floor of Congress are recorded in the following publications:
The Congressional Record is published in a newspaper-style daily edition (and, until 1985, a biweekly edition), then renumbered and recompiled into a bound (hardback) permanent edition at the end of each legislative session. Bluebook Rule 13.5 tells you to cite the daily edition only if the permanent edition is not yet available.
Although free versions of the Congressional debates can be somewhat clunkier to navigate, you can also access complete PDFs of Congressional debates for free online:
Both Lexis and Westlaw provide access to Congressional debates, although they generally do not offer a significant advantage over the free options. However, if you would like to search copies of the Congressional Record (Daily Edition) from 1985 forward by keyword, Lexis and Westlaw do allow you to perform more sophisticated keyword and terms and connectors searching.
The Congressional Record includes two indexes:
Generally, the most efficient way to use the indexes is to access the permanent edition for the relevant year on HeinOnline or GovInfo. Look at the end of the permanent edition for sections labeled index and history of bills. Each index entry will refer you to the relevant page numbers within the permanent edition.
GovInfo omits the index and history of bills from the permanent edition beginning in 1999. Instead, from 1983 forward, GovInfo provides separate pages for the index and history of bills:
These separate pages provide citations to the Daily Edition in the format PAGE [DAY MONTH]. (E.g. S5798 [9JN] means page 5798 of the Senate section of the June 9th daily edition, while H4359 [18MY] means page 4359 of the House section of the May 18th daily edition.)
For recent years, they can be useful tools because each citation is directly linked to the relevant pages of the Daily Edition. However, they are less useful for older years, where they often omit citations entirely and where only the permanent edition is available on GovInfo. Additionally, keep in mind that if you are using Bluebook citation format, you will ultimately need to cite to the permanent edition.
For all these reasons, using the index and history of bills in the permanent edition is the better choice, except for very recent debates that have not yet been published in the permanent edition.