When you're looking for specific documents, your best bet is to track down a reputable scholarly source, and look at the footnotes to see where they got their primary source (the original document). If you're starting with a popular history book or textbook, it's likely that they're going to reference a secondary source, rather than a primary source. If you find this, you just have to track the chain of citation back to someone who cites it as a primary source. Sometimes it dead ends. Sometime the original citation looks nothing like what someone three citations later says it looks like. Looking into these things to decide for yourself is a big part of doing history rather than just consuming it. So, if we look at a recent article discussing the Negro Seamen's Act(s)

Tyler, J. H. (2016). The unwanted sailor: Exclusions of Black sailors in the Pacific Northwest and the Atlantic Southeast. Oregon Historical Quarterly, 117(4), 506-535.

and find the specific place where the author discusses South Carolina's 1822 law, (page 508) we find a long footnote:

8. Although the multiple anti-black sailor laws possessed different names at times, they are collectively referred to in this article as the Negro Seamen Acts. For discussion of black American sailors in the Atlantic during the antebellum period, see Peter Linebaugh and Marcus Rediker, The Many-Headed Hydra: Sailors, Slaves, Commoners, and the Hidden History of the Revolutionary Atlantic (Boston: Beacon Press, 2000); Michael Alan Schoeppner, “Navigating the Dangerous Atlantic: Racial Quarantines, Black Sailors and United States Constitutionalism,” (Ph.D. diss., University of Florida, 2010); Philip Hammer, “Great Britain, the United States, and the Negro Seaman Acts, 1822–1848,” Journal of Southern History 1:2 (May 1935): 3–28; Harold D. Langley, “The Negro in the Navy and Merchant Service, 1789–1860, 1798,” Journal of Negro History 52:4 (October 1967): 273–86; Alan January, “The South Carolina Association: An Agency for Race Control in Antebellum Charleston,” South Carolina Historical Magazine 78:3 (July 1977): 191–201; Bolster, “ ‘To Feel Like a Man’: Black Seamen in the Northern States, 1800–1860,” Journal of American History 76:4 (March 1990): 1173–99; and Alan Taylor, The Civil War of 1812:
   American Citizens, British Subjects, Irish Rebels, & Indian Allies (New York: Vintage, 2010).

If you're interested in finding the original primary source, I'd usually recommend working from oldest date of publication forward. So, if we take:

Hamer, P. M. (1935). Great Britain, the United States, and the Negro Seamen Acts, 1822-1848. The Journal of Southern History, 1(1), 3–28. https://doi.org/10.2307/2191749

We see that the author cites the actual law in footnote 4:

"Acts . . . of the State of South Carolina . . . 1822 (Columbia, 1823), 11-14"

That's a pretty standard format for referring to legislative records, the [...] just is skipping over "and resolutions of the General Assembly of" and "passed in". Various states and the federal government will all have slightly different ways of organizing and referring to their records, and the exact format also changed over time. South Carolina has digitized some of their records here.

https://www.carolana.com/SC/Legislators/Documents/home.html

However, the entry for 1822 is missing from this digital resource. The larger reference text for 1814-1838 gives the name of the law: "An act for the better regulation and government of free negroes and persons of color, and for other purposes" on page 179, and shows that it was passed in 1822, but it doesn't recount the full text of the act. For that we'd need the volume specific to 1822, but it hasn't been digitized. We need a physical copy, and that probably involves going either to a state archive (though keep in mind for future questions that many Antebellum Southern documents were lost in the Civil War) or to a USC research library. But again, that's part of doing history. Contrary to other disciplines where everything you'd ever want to read is online, the archive, the library, and physical materials more broadly are still a critical part of historical scholarship.

Federal Laws are a bit easier in the sense that they're more centralized, and important ones are more likely to be digitized. The Morrill Act and the Revenue Act of 1861 were pretty easy to find with a quick google search. That said, you may still have to follow the research process outlined above to track down the occasional obscure law.