Welcome to the Ranch
Try community server and connector/J, available here. On Linux/Unix you want the "client" files as well. There is a reference manual and chapter 3 includes a tutorial. Note the installation instructions (chapter 2) must be followed very carefully, as must the instructions about where to put the connector files.
On Windows the easiest way to get started is to download the MSI Installer and run it - it will set up the mysql service and guide you through setting up the initial database.