The Library Manager is a newer feature of the Arduino IDE. Many of the popular libraries, including most of Adafruit's, are in the Library Manager. If you are looking to work with other people's libraries, first check the Library Manager to see if the library is there first rather than downloading a copy into your local libraries folder.
To start, load the Arduino IDE. Then use the menus at the top to select Sketch -> Include Library -> Manage Libraries...
You will then get a list of all the great libraries you can install!
Most often you may use the Search features at the top to find a specific library.
Above, the user typed adafruit into the search bar. All modern Adafruit libraries begin with the word Adafruit.
You can scroll down the list to find the library you are looking for. Say we wanted the Circuit Playground library like shown below. You can click the Install button to have it available or is it is already installed, you can select the version you want (often the latest but sometimes an earlier library for compatibility).
Often (but not always), loading a library will bring the availability of additional examples. In the menu, go to Files -> Examples then select your library name (if present) and browse the additional examples. Loading the Adafruit CircuitPlayground library above also loaded 12 examples and 4 directories with additional examples.
The latest versions of the Arduino IDE will alert you on startup that newer versions of your installed libraries (and boards) are available, if you would like to upgrade. You can safely ignore these in a pinch but you'll want to get the latest libraries when you start a new project.