Just a bit of all around info wrapped here...
Permissions issues usually are caused by 2 main reasons:
- Real file/folder permissions issues on the OS
- Wrong directory paths for the tmp/log directories, defined in the configuration file.
The best way to see if there is actual a permissions issue is to check in the backend:
System Information -> Directory Permissions.
This will tell you which files/folders in the root of your Joomla installation are writable (green color), or not writable (red color).
For case 1 - One of the easiest ways, to deal with wrong permissions assigned on file/folders by the operating system, is to use Akeeba's Admin Tools. It provide a utility to setup your desired permissions and apply to all folders/files of the Joomla installation.
For case 2 - In the case you have wrong paths defined for tmp/log directories, you should change this in the global configuration of Joomla. If you don't know what your hosting's home directory is, it's better to ask your hosting provider.
You can edit these path either from the backend of Joomla in Glogal Configuration, or via the file manager of your hosting or connecting with FTP, and editing the configuration.php file.
Usually in cPanel hosting, this is like:
So the final look for these settings in your configuration.php file should be like:
public $log_path = '/home/myHostingUsername/logs';
public $tmp_path = '/home/myHostingUsername/tmp';
*Be aware, that this is one of the most common "mistakes" Joomla beginners do. They forget to change these paths in their configuration
file, after moving their sites from another host, a subfolder or from
their localhost, resulting these directories to be unwritable.