Apparently you already have some Laravel application and some server or shared hosting. Now you need to automate the process of deployment. Deployer will helps you in this as it ships with some ready to use recipes for Laravel based application.
They start with the details about installing the tool then share the single "dep init" command to create the deployment configuration needed to deploy a default Laravel application. There's a few modifications you'll need to make for your own project (like repository location, server information and the path to your SSH key) but that's basically it. The "dep deploy" command can then be used to push the release to the remote server in a "current" directly ready and waiting for your web server to serve up.