You have to have a server installed on your computer (Xamp, Wamp, Linux etc.). Make sure to meet the requirements for Laravel installation: check Laravel version in composer.json file and then check in the documentation of Laravel which version of PHP and other tools you need. The course was made in Laravel 5.5. Install Laravel using this version. Later in the upgrade guide I will show you how to upgrade Laravel to the next minor and major versions (including Laravel 6).
Follow exactly what I say and do and you will have the same app on your computer.
Remember that only practice makes perfect. If necessary, study the course two or more times. Take notes during the course like a real student. Use documentations, Google search. Finally, try to write the application yourself, not necessarily the same as in the course, you can try to change, add something, etc. No single course will make you a very good web developer. It can only bring you closer to this goal. The more practice, the better.