Here is a simple example to load up some nodes of type event for the month of March, looking up information of a field type datetime called 'field_date':

drupal-query.php

<?php

<?php
  $query = new EntityFieldQuery();
  $entities = $query->entityCondition('entity_type', 'node')
                    ->entityCondition('bundle', 'event')
                    ->propertyCondition('status', 1)
                    ->fieldCondition('field_date', 'value', array('2011-03-01', '2011-03-31'), 'BETWEEN')
                    ->fieldOrderBy('field_date', 'value', 'ASC')
                    ->execute();

  $nodes = node_load_multiple(array_keys($entities['node']));
  $views = node_view_multiple($nodes, 'teaser');
  $build['#nodes'] = $views['nodes'];
  $build['#theme'] = 'whatever';

  return $build;
?>