To get started with building a Salesforce frontend using Vue, run cd ./force-app/ui
and make sure to have all dependencies of the frontend installed, by running npm install.
To start the local dev server, first connect it to a Scratch Org to be able to access Apex classes from your Vue application.
Prerequisite, use SFDX to create a scratch org and push this project to it.
Run npm run sf:connect to connect your backend.
Start the webserver by cd ./force-app/ui and npm run dev.
To build the frontent assets and publish them into the Static Resources directory:
Run cd ./force-app/ui and npm run build.
After this completes, you should be able to push the static resource to your org using SFDX.