There are many different ways to set up your MySQL database. It really depends on the type of platforms you are running, whether it is Windows, Linux, Mac, or any other type of operating system; it will also depend on the purpose of your database—whether it's for development and testing, or for a large-scale production server.
For large scale services (such as social media), the best way is to compile MySQL from the source, because such as project requires a ton of optimization, configuration, and sometimes customization in order to handle the large amount of users and traffic.
However, you can just download the pre-compiled binaries if you're going for normal use, as the default configuration is pretty sufficient for that. You can install a standalone MySQL installer from their official website or the download installation packages...