Once you have a MongoDB connection instance, you can execute a MongoDB commands and queries using yii\mongodb\Command:
// execute command:
$result = Yii::$app->mongodb->createCommand(['listIndexes' => 'some_collection'])->execute();
// execute query (find):
$cursor = Yii::$app->mongodb->createCommand(['projection' => ['name' => true]])->query('some_collection');
// execute batch (bulk) operations:
Yii::$app->mongodb->createCommand()
->addInsert(['name' => 'new'])
->addUpdate(['name' => 'existing'], ['name' => 'updated'])
->addDelete(['name' => 'old'])
->executeBatch('customer');
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();