In Magento 1, logging was pretty simple, we add Mage:log($var, null, 'test.log'); anywhere you needed to know something.

With dependancy injection in Magento 2, things are a little different.

There are two main ways to log things.

Injecting \Psr\Log\LoggerInterface or using the \Zend\Log\Writer class.

Normally, if the logger is already injected, I’ll just hijack it and use it:

$this->logger->debug($var);

If not, just declare it as a dependancy in the constructor of the class and use it:

protected $logger;

public function __construct(\Psr\Log\LoggerInterface $logger)
{
    $this->logger = $logger
}

Then you can use where ever you need to log like so:

$this->logger->debug($variable);

There are multiple log levels associated with Psr Logger they can be found in LoggerInterface and are listed below:

public function emergency($message, array $context = array());
public function alert($message, array $context = array());
public function critical($message, array $context = array());
public function error($message, array $context = array());
public function warning($message, array $context = array());
public function notice($message, array $context = array());
public function info($message, array $context = array());
public function debug($message, array $context = array());
public function log($level, $message, array $context = array());

Also, keep in mind Psr Logger can only log strings not arrays or objects. One can get around this by using print_r($array, true) as $message to print arrays, this can also be done with the Zend Logger below as well.

My favorite way to log however, especially during troubleshooting is as follows:

$writer = new \Zend\Log\Writer\Stream(BP . '/var/log/test.log');
$logger = new \Zend\Log\Logger();
$logger->addWriter($writer);
$logger->info('Your text message');

You can also use the Zend Log when you are outside the scope of \Psr\Log\.

How do you know if the logger is already injected?

Look for the $logger variable in the class you are attempting to log from, and in the constructor.

 /**
  * @var \Psr\Log\LoggerInterface
  */
 protected $_logger;


 public function __construct(
         \Magento\Framework\Model\ResourceModel\Db\Context $context,
         \Magento\Store\Model\StoreManagerInterface $storeManager,
         \Magento\Eav\Model\Config $eavConfig,
         Product $productResource,
         \Magento\Catalog\Model\Category $catalogCategory,
         \Psr\Log\LoggerInterface $logger,
         $connectionName = null
     ) {
         $this->_storeManager = $storeManager;
         $this->_eavConfig = $eavConfig;
         $this->productResource = $productResource;
         $this->_catalogCategory = $catalogCategory;
         $this->_logger = $logger;
         parent::__construct($context, $connectionName);
     }

If this is the case, then just hijack it and use:

$this->logger->debug($var);

Lastly, to ensure logs are translated accoringly, wrapping them in the __() function is always a good idea and can be done as follows:

$this->logger->critical(__("Message to log Error: %1", $exception->getMessage()));

The above will translate the message and also parse the getMessage() function if you add it in a catch block.