For Linux systems, if it's possible, I recommend that you install MySQL using whatever package management system is available to you. Perhaps go for YUM, if you're using a Red-Hat-based distribution, APT if you're using a Debian-based distro, or SUSE's repository system. If you do not have a package management system, you may need to install MySQL from the source.
Windows users can install MySQL directly from their website. You should also be aware that MySQL comes in 32-bit and 64-bit binaries, but whatever program you download will likely install the correct version for your system.
Here is the web page from where you can download MySQL for Windows:
I recommend that you use the MySQL Installer. Scroll down, and when you're ...