How do I load a third party PHP library?
The 8.x-3.x branch of the Libraries module still provides the libraries_get_path() function. And (as of now) it looks pretty much unchanged. So you should be able to use it in the same way.

As far as where to put your library, the libraries_get_libraries() function has been updated with the following addition to the $searchdir array:

// Always search the root 'libraries' directory.
$searchdir[] = 'libraries';


Which indicates that you can place your libraries in a directory named "libraries" at your site root.