Here are some ways of including the library in your addon.

Using an automated packager is the preferred method of embedding the library, as it takes out the overhead of maintaining the latest library version with the addon. By either using CurseForge's or BigWigs', you could use some simple metadata markup for retrieving dependencies.

Simply plop the this in to your .pkgmeta file and you're off to the races!

externals:
  libs/LibStub: # required dependency
    url: https://repos.curseforge.com/wow/libstub/trunk
    tag: 1.0
  libs/LibProcessable:
    url: https://github.com/p3lim-wow/LibProcessable
    tag: latest

See this article for more information.

Either by using gitmodules, subtrees or manually cloning or downloading the archive and extracting, the library can be handled manually if you prefer that.

In order for the library to load, it must be loaded from the addon.
Here's an example TOC file:

## Interface: 80000
## Title: MyAddOn

libs\LibProcessable\LibProcessable.lua

...