Typically, you will code everything locally in the editor of your choice, with a web server running on your local machine—preferably one that is configured (nearly) identically to the production server. In the Laravel community the most popular options are Valet and Homestead.
To deploy, most developers push the code to a Git repository, from which it is pulled to staging and/or production servers via "hooks". Ideally, this will also trigger the server to run Composer commands to install dependencies and optimize the codebase.