deploying a Laravel + vuejs project is the same as deploying vanilla Laravel. You just need to ensure you have built your app.js before publishing.
Details from digital ocean https://www.digitalocean.com/community/tutorials/how-to-deploy-a-laravel-application-with-nginx-on-ubuntu-16-04
my steps
- push to hosting
- run composer to install vendor packages
- set permissions for logs and storage directory
- set up db + add settings .env
- run artisan migrate to install db tables.
- point webroot to /public/index.php