1 - Remove vendor and node_modules folders, later we'll install them on host.
2- Now let's imagine your host folders like this:
/home
/home/public_html.
3- In /home upload your project, now it's /home/my-project.
4- Now copy files in /my-project/public and paste it in /home/public_html or if you've another domains maybe to /home/public_html/my-project.com.
5- Login to your host with suitable ssh mean and cd to your project directory and run composer install.
6- The last important change on your code is in /home/public_html/index.php , you should change
require __DIR__.'/../bootstrap/autoload.php';
$app = require_once __DIR__.'/../bootstrap/app.php';
to
require __DIR__.'/../../my-project/bootstrap/autoload.php';
$app = require_once __DIR__.'/../../my-project/bootstrap/app.php';
I think that's all you need.