Joomla strikes again - 3.4.0 and Protostar template

Recently Joomla backend started to notify you that there is an update to 3.4.0 is available, you're updated it (without backing up your site, of course) - and your pages based on beautiful Protostar template became damaged...Some modules become thin and long and overlap with each other... If this is your case, read how to deal with it losslessly.