The United States Code (U.S.C.) is the official source of the general and permanent laws of the United States, organized by subject matter. The U.S. Code is published by the Office of the Law Revision Counsel of the U.S. House of Representatives. It is published every six years and updated in the interim with annual bound cumulative supplements.
The U.S. Code is divided by subject matter into 51 "Titles." Code titles are then divided into chapters, which are further divided into sections. Only the title and section numbers are used to cite to particular code sections.
For example, if you were looking for the statute that prohibits debt collectors from harassing consumers: Title 15 covers "Commerce and Trade" but is subdivided into 110 chapters; chapter 41 covers "Consumer Credit Protection" and is subdivided into 6 subchapters; subchapter V covers "Debt Collection Practices" and consists of sections 1692 - 1692p; section 1692d covers harassment and abuse, so the citation would be 15 U.S.C. § 1692d.
In addition to the official version of the U.S. Code, there are annotated versions of the Code published by West (U.S. Code Annotated) and Lawyer's Co-operative/Lexis (U.S. Code Service). The annotated versions of the code are more useful for research purposes, as they generally contain references to additional primary and secondary sources.
State codes (sometimes called "statutes") vary greatly. In many instances they are now published by commercial publishers. Some states may have official and unofficial versions of the state code, others may only have one version. Find the exact title of the state's published code and session laws from table T1 of the Bluebook.
In New York, the New York Code is entitled McKinney's Consolidated Laws of New York Annotated