You can first start working on an web application using laravel on your local , have the entire setup on your local using xamp , compose the code using composer . Once the code is ready to deploy. you can choose an EC2 instance and setup a sever based on your need and launch the server by setting up a pem file by converting the pem file to ppk using puttygen.
you can login to the AWS server using the ppk file, install the apache, mysql and php , do the necessary setting in the apache. install phpmyadmin so that you can login to the mysql from browser or you can login via command line using putty. enter the ip address you will see the apache default page and that file is index.html which resides in docroot and is located in /var/www/html in ubuntu.
you can zip the local laravel project and upload it there from command line or using client FTP winscp or filezilla. export the mysql database from local and import it on the AWS server and make the necessary changes pointing database the correct database and credentials, re-writing the new .htacces file. once all of these are in place your laravel application will be working like a charm.
If you need any help or assistance let me know.
Hope this helps