If you've ever stumbled across CLIA statute and regulations, they're actually pretty dry and short.
Lab shall have appropriate management, appropriate staff, appropriate controls, and so on. Read about CLIA law, history, and links to laws and regulations here.
Where you get a lot more detail is Medicare's 400-page manual for CLIA inspectors, last updated in 2017.
Regarding CLIA lab administrative details, see also the lab inspection special manual, Chapter 6, 256pp, here.
The explosive CLIA inspection of Theranos plays a big part in the final reel of the 8-part Theranos drama, Dropout, on Hulu, here.
Nerd note. The original CLIA regulations in 1967 emerged after scandals related to Pap smears. If I recall correctly, CLIA 1967 applied only to interstate labs and labs accepting federal Medicare money. (Perhaps not certain if there was constitutional authority to regulate in-state labs not crossing a state line...thus, putting CLIA under the interstate commerce authority of the Constitution). CLIA 1988 applied more broadly to all labs.