Various tips and tricks

Use Find usages of PhpStorm for examples! The source code of the Core is a great way to learn how specific methods of the API are used. In PhpStorm it is extremely helpful to right-click on a single method and list all method usages with Find usages. This is especially handy to quickly see usage examples for complex methods like join() from the query builder.
INSERT, UPDATE and DELETE statements are often better to read and write using the Connection object instead of the query builder.
SELECT DISTINCT aField is not supported but can be substituted with a ->groupBy('aField').

getSql() and executeQuery() / executeStatement() can be used after each other during development to simplify debugging:

EXT:my_extension/Classes/Domain/Repository/MyRepository.php

$queryBuilder
    ->select('uid')
    ->from('tt_content')
    ->where(
        $queryBuilder->expr()->eq(
            'bodytext',
            $queryBuilder->createNamedParameter('lorem')
        )
    );

debug($queryBuilder->getSql());

$result = $queryBuilder->executeQuery();

Doctrine DBAL throws exceptions if something goes wrong when calling API methods. The exception type is \Doctrine\DBAL\Exception. Typical extensions should usually not catch such exceptions but let it bubble up to be handled by the global TYPO3 core error and exception handling: They most often indicate a broken connection, database schema or programming error and extensions should usually not try to hide away or escalate them on their own.
count() <database-query-builder-count> query types using the query builder normally call ->fetchOne() to receive the count value. The count() method of the Connection object does this automatically and returns the result of the count value directly.