"Private Laws" are laws that affect only specified individuals or entities, as opposed to Public Laws, which affect everyone in the jurisdiction.
To get Federal Private Laws: Private Laws are published in print as Slip Laws, and they have published chronologically in Statutes at Large since 1789. Slip Laws and Statutes at Large are available in most academic and Federal Depository Libraries.
Private Laws are posted on Thomas back to the 101st Congress (1989-90) and FDsys back to the 104th Congress (1995-96). They are also available in Statutes at Large (see "Statutes At Large").
You can search for Private Laws on Lexis in the Statutes at Large file (LEGIS;STATLG); add "and HEADING(Private Laws)" to the end of your search string to retrieve only Private Laws. If you have a citation, you can pull a law or other document using the format: "99 Stat 1761".
You can get very recent Private Laws by calling the Legislative Resource Center (formerly the House Document Room) at 202-226-5200. If you aren't in D.C., they will mail them, or you can hire a document retrieval service to pick them up.
Private Laws are not codified in the U.S. Code, and they are not published in USCCAN.
Annotations: You can find judicial opinions, law review articles and other sources citing a Federal private law by Shepardizing the Statutes at Large cite on Lexis.
Citation: Federal Private Laws are cited as "Priv. L. No." (e.g., Priv. L. No. 105-1).
Indexing: As far as I can tell, Private Laws are not indexed by anyone, anywhere, ever.
Legislative History: Private laws can have legislative history just like Public Laws. You can link to some legislative history materials through Thomas. For a comprehensive list of additional reports and documents, see the CIS U.S. Serial Set Index.
For more about Private Laws, see "Private Bills and Private Laws," 99(1) Law Library Journal 87 (Winter 2007), by Matthew Mantel and The Decline of Private Laws
by Melanie Buck.