Assuming you have a VPS server running Apache (or whatever else) with a a properly configured vhost and terminal (ssh) access, if you want deploy a Laravel app there, you surely need to
- Copy all project files, except for the vendor directory, from localhost to your server
- Verify file ownage and access rights (chown/chmod)
- Change all necessary config
- run a
composer update
- run
php artisan migrate to create the database scheme
- clear cache
php artisan cache:clear
Next thing is populating the database with your apps data from localhost. You can either do it manually (dump sql local, import it on server), or if you want Laravel for it you can use Seeding (Laravel docs).
There even is a nice package that let's you automaticaly generete Seeders from your current database content - so it's very useful for the purpose of moving the app to another server.
https://github.com/orangehill/iseed
Inverse seed generator (iSeed) is a Laravel 4 package that provides a
method to generate a new seed file based on data from the existing
database table.
EDIT
If you are using a shared hosting account, check out this guide
http://driesvints.com/blog/laravel-4-on-a-shared-host
This post from Laravel forum might also be of use
http://forums.laravel.io/viewtopic.php?id=9639