The repository should be cloned into the steam installation folder for Project Cars 2. If you installed in the default location on drive C this would be C:\Steam\steamapps\common\Project CARS 2\ and the complete parth to the files would be C:\Steam\steamapps\common\Project CARS 2\Vehicles\Textures\CustomLiveries\.
If your file manager prompts you to overwrite existing files you want to say yes, as the default skins are blank white templates and will need to be overwritten.
NOTE: Currently if you clone the repo it will also download the Screenshots and Documentation.
Project Cars 2 only allows skin substitution for one variant of each car. Chris has in some cases produced multiple replacement skins for the same vehicle. Any of the skins that have a number after the word livery in the filename are a variant, but only one will be picked up by the game and that will be the one that does NOT have a number.
As an example there are multiple Ford Mustang RTR skins included currently:
ford_mustang_rtr_formula_drift_livery.dds
ford_mustang_rtr_formula_drift_livery2.dds
ford_mustang_rtr_formula_drift_livery4.dds
You will need to place the one that you want into the games folder, and if it's one of the variants, you will need to rename it so the number is removed after livery.
I have put the screenshots on their own page, this is mostly so you don't have to load 40+ images to read the installation instructions.
These car skins were made by and © Chris Broomfield, AKA Horsewood and kindly shared.