The basic physics
The "known substance" is usually indocyanine green, a benign dye which is strongly protein bound and has a very rapid (~ 150sec) hepatic clearance.
Dye dilution concentration over time curve
Data from this measured concentration curve can then be used to plug into the Stewart-Hamilton equation. George Neil Stewart first described it in 1897, after some animal experiments. His subjects were dogs, and his indicator was sodium chloride.