Carreyrou originally got tipped off by pathologists saying that this was impossible, then they got sued into oblivion (see thepathologyblawg).
(IANAP but this is my understanding)
Some real tests rely on having a huge blood sample (e.g. 100ml), being filtered (e.g. by centrifuge) and then a test of a known sensitivity applied.
Theranos claimed that their tests were more sensitive so could work with smaller samples. Statistically this doesn't work because with a finger-prick test (e.g. 1ml) the sample is 100x less likely to contain the target cells - cells are integers.
Additionally finger-prick tests contain only capillary blood - they're filtered by the finger blood vessels only allowing tiny cells - some of the Theranos tests claimed they could detect markers that only exist in arterial and venous blood.
(I do realize that keeping track of how precisely Theranos was lying can be frustrating, since they were doing multiple levels of lying here.)
Longer answer: Theranos never really got their own custom machines working. Until those machines were working, they did use other machines and processes which did work. However, their entire shtick was trying to do a lot of tests on less blood than usual, so... they simply diluted the blood samples to get enough volume for those machines to function in the first place, and correspondingly, the results were absolute garbage. Effectively, they were using working machines incorrectly to cover up for their non-working machines.