How to migrate old J prefix classes to new Joomla classes

You need to specify the namespace before you use them, so for your examples above:

use JoomlaCMSLanguageText;
use JoomlaCMSMVCControllerBaseController;

class YourClass extends BaseController {
    echo Text::_('YOUR_CONSTANT');
}

Otherwise, you can do it like this, which is going to get tedious pretty quick:

class YourClass extends JoomlaCMSMVCControllerBaseController {
    echo JoomlaCMSLanguageText::_('YOUR_CONSTANT');
}