How to debug a query in extbase?

In version 8.7 or newer another way needs to be taken:

use TYPO3\CMS\Extbase\Persistence\Generic\Storage\Typo3DbQueryParser;
use TYPO3\CMS\Extbase\Utility\DebuggerUtility;

$queryParser = $this->objectManager->get(Typo3DbQueryParser::class);
$queryBuilder = $queryParser->convertQueryToDoctrineQueryBuilder($query);

DebuggerUtility::var_dump($queryBuilder->getSQL());
DebuggerUtility::var_dump($queryBuilder->getParameters());

This information is outdated and deprecated in TYPO3 8.7 and I'm only leaving the answer up for reference. Refer to @pgampe 's answer on how debug extbase queries in more recent versions of TPYO3.

Extbase now has a QueryParser for that. In your repository method, right before returning the executed query, insert:

    $parser = \TYPO3\CMS\Core\Utility\GeneralUtility::makeInstance('TYPO3\\CMS\\Extbase\\Persistence\\Generic\\Storage\\Typo3DbQueryParser');  
    $queryParts = $parser->parseQuery($query); 
    \TYPO3\CMS\Core\Utility\DebugUtility::debug($queryParts, 'query');

The result is a table view of the query parts, split by SQL keywords, e.g.:

Keep in mind that the QueryResult that your Repository returns may still be different from the SQL query result. Extbase uses the PropertyMapper to try to convert every result row into an ExtbaseObject. If the PropertyMapper is misconfigured or the row contains data that cannot be converted to the data types according to the configuration, these Objects will silently be skipped.

$query = $this->createQuery();
$result = $query->matching($query->like('linker', "$linkerKey=$linkerValue"))
   ->setOrderings(array('crdate' => $ordering))
   ->execute();

$GLOBALS['TYPO3_DB']->debugOutput = true;

return $result;