Congressional debates are recorded in the Congressional Record. The Congressional Record provides a verbatim transcript of what is spoken on the floor, although members have the right to revise and extend their remarks before they are printed, and to submit additional prepared statements to be included in the record. (Beginning in 1978, a black dot has been used to signify statements that were not actually spoken by the member on the floor.)
In addition to providing a written record of what is spoken on the floor of Congress, the Congressional Record also contains a "Daily Digest" section that lists the bills introduced and considered, reports released, votes taken, and committee meetings and hearings held each day. Accordingly, the Congressional Record allows you to track legislative activity with respect to a particular bill on a daily basis.
There are two versions of the Congressional Record: the daily version and the permanent bound version. The daily version is printed every day that Congress is in session and indexed every ten days to two weeks. It is divided into four sections, each with its own separate pagination: House, Senate, Extension of Remarks, and Daily Digest (e.g., H555, S1001, E777, D333). The index allows access by subject, name of legislator, title of legislation, and bill number.
Several years after the conclusion of a Congressional session, the various daily editions are consolidated into a permanent bound set with a cumulative index. When this is done, the separate section pagination is eliminated and replaced by one continuous sequence with no letter designation. Most citation guides, including the Bluebook and the Maroonbook, require that citations be to the permanent bound volumes, unless the material cited has not yet been published in the bound version.
The University of California at Berkeley Library has created this online tutorial showing how to find floor debates from 1873-present.