Take a look at the Magento Webservices Introduction page on the Magento Wiki if you're not sure how to connect and use the Magento API.
The config API provides three methods, here are is some PHP to get you going:
Read
$client->call($session, 'config.read', array('CONFIG_KEY'));
Set
$client->call($session, 'config.set', array('CONFIG_KEY', 'NEW_VALUE'));
Delete
$client->call($session, 'config.delete', array('CONFIG_KEY'));