I covered this section in a previous post, here:
So, the actual deployment process was only a case of updating the files and database.
Update the files
After I finished all the work on my localhost, I deleted everything within the public server and kept only the .env file, as it has the public database credentials and the APP_URL.
Then, I zipped up all my local files again, uploaded the .zip file and extracted it on the server.
Update the Database
Similarly, I wiped off all the columns from my SQL database in the public server and export/import a fresh copy of my local one, up there.
Refreshed the page and everything worked as it should: https://laravel.appsology.co.uk/