MySQL is available from multiple sources. It might be a part of your Linux distributions available software or already built into your virtual image if you are using something like Laravel's Homestead. MySQL runs on most of the popular operating systems. And it is highly recommended to start off at MySQL :: MySQL Downloads to get the latest and greatest. Don't be intimidated by the man options available to you. Most people start with the MySQL Community Edition server MySQL :: MySQL Community Downloads
The MySQL Community Edition is a freely downloadable version of the world's most popular open source database that is supported by an active community of open source developers and enthusiasts. So you can try it without a financial investment. If you later determine that MySQL is not for you then you can easily delete it without a twinge of pain in your wallet.
As of the writing of this post (Early December 2015) the latest release of the Community Server is 5.7.10. Download the binaries for your operating system. The source code is also available for those who want to compile their own server complete with detailed instructions. The WIndows version comes as a MSI installer, my preference, or a zipped file and comes with tools like MySQL Workbench.
This will save you time and frustration later on and helps avoid problems like running out of disk space or trying to install on a very old operating system version. This is also a wonderful introduction to the amazing MySQL Manual.
So go download and install. Next time we will load some test databases and start to use MySQL.