Using the connection instance you may access databases and collections. Most of the MongoDB commands are accessible via yii\mongodb\Collection instance:
$collection = Yii::$app->mongodb->getCollection('customer');
$collection->insert(['name' => 'John Smith', 'status' => 1]);
To perform "find" queries, you should use yii\mongodb\Query:
use yii\mongodb\Query;
$query = new Query;
// compose the query
$query->select(['name', 'status'])
->from('customer')
->limit(10);
// execute the query
$rows = $query->all();
This extension supports logging and profiling, however log messages does not contain actual text of the performed queries, they contains only a �close approximation� of it composed on the values which can be extracted from PHP Mongo extension classes. If you need to see actual query text, you should use specific tools for that.