Assuming you're using ES6 and a bundler such as Webpack you can start using Fabric.js as follows:

At the command line

npm install fabric

or

yarn add fabric

Then import it in your .js file.

import { fabric } from 'fabric'

Then set up your Canvas in Vue's mounted: method.

Note: For me the default fabric npm module resulted in quite a large package. I ended up using the fabric-browseronly module instead. Fabric.js has a lot of features you might not need, in which case you could build your own version here or via the command line.