Usage is easy, just use the helper:
// Log data
Mage::helper('logging')
->setData($data)
->log();
// Log a message
Mage::helper('logging')
->setMessage('My message')
->log();
Mage::helper('logging')
->setTypeOk()
->setMessage('Different type')
->log();
Types: NOT_SET,OK, INFO, WARNING, ERROR
