Transferring Joomla! website from live server to local webserver might cause some issues or errors due to the different webserver configuration. You can use common local web server applications such as XAMPP, WAMP or MAMP to host Joomla! website. This tutorial will discuss the configuration that needs to be modified if you transfer your Joomla website from live to a local webserver. 

Disable Deprecated Extension
This might cause some issues related to the deprecated extension eg if your live web server uses PHP 5.6 or 7, then in your local use PHP 8, it may cause some issues related to the compatibility. To disable the deprecated extension, you can simply configure it directly from the live server Joomla website. However, if you need to manually disable the extension, you can navigate to the database table 'xxx_extensions' and find the deprecated extension and disable it.

General Configuration
The following general configuration can be modified directly from the configuration.php file as shown below:

public $host = 'localhost';
public $user = 'root';
public $password = '';
public $db = 'yourLocalDBname';
public $live_site = '';

If you need detailed error reporting, set it to maximum.

public $error_reporting = 'maximum';

That's all. Happy coding :)