This is a normal fedora, so a simple
sudo dnf install mysql
will install a MySQL server. Done!
(You might notice that the package you're getting might be called mariadb, but that doesn't change the fact you're getting MySQL. It's just that the software that is now called "MySQL" is a fork of the original MySQL under a different license for commercial reasons of Oracle. "MariaDB" is the continuation of what is originally called "MySQL". If you want a LAMP setup, you generally want MariaDB, not the new MySQL, unless you have an expensive service contract with Oracle – but then you wouldn't come here for installation advice, but use their service, I guess.)