Drupal - 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.

Composer:

Composer is a tool for dependency management in PHP. It allows you to declare the dependent libraries your project needs and it will install them in your project for you.

plus the Composer Manager module:

Composer Manager provides a gateway to the larger PHP community by enabling Drupal modules to more easily use best-in-breed libraries that are managed by Composer.

can handle this.