In order to connect to the free edition you should open the File Explorer from the View menu option. Then right click on the Relational DB and select New Server. Database Type should be MySQL Community Edition. Driver Classpath should point to the MySQL JDBC driver jar file, Server URL should be //<host>:<port>/<database>? e.g. //localhost:3306/mydb?. The trailing question mark is necessary.
If the connection still does not work then can you post the error message displayed? Stylus Studio is usually pretty detailed in the error message and will show you the stack trace.