Javascript libraries are collections of code that have been developed for re-use (jQuery, for example, is a javascript library). For most libraries, simply link the code file (through a cdn, or locally) in your html document prior to your site’s js. For libraries that are built off of jQuery (they usually say so in their documentation), make sure to link your jQuery file before listing your additional library.
Below is a brief list of js libraries to get you started. Many js libraries are built to aid with layout and functionality, others are built to help animate, provide certain visual styles, or render more advanced graphics.