I have Oracle SQL Developer already installed and am able to connect to and query Oracle databases.
Using Help -> Check for Updates I was able to install the Oracle MySQL Browser extension but there are no connection options for MySQL databases.
Under Tools > Preferences > Databases there is a third party JDBC driver path that must be setup. Once the driver path is setup a separate 'MySQL' tab should appear on the New Connections dialog.
Note: This is the same jdbc connector that is available as a JAR download from the MySQL website.