Public laws have general applicability nationwide. Private laws apply to indiviuduals, for example immigration and naturalization.
After the President signs a bill, the Office of the Federal Register, National Archives and Records Administration (NARA) assigns it a law number, and prepares it for publication as a "slip law."
At the end of each session of Congress, the OFR compiles the slip laws into bound volumes called the Statutes at Large. The Statutes at Large contains session laws in the order in which they were enacted.
There are a number of sources that contain Public Laws and Statutes at Large.