In your case, you can probably simply query the field data table, with a condition on the entity type and bundle.
In any case, something like:
$field_name = 'FIELD_NAME';
$result = db_select("field_data_{$field_name}", 'f')
->fields('f', array('entity_id', "{$field_name}_value"))
->condition('entity_type', 'node')
->condition('bundle', 'article')
->condition('deleted', 0)
->range(0,10)
->execute();
foreach ($result as $row) {
// drupal_set_message($row->field_name_value); // example
drupal_set_message('<pre>'.print_r($row,1).'</pre>');
}
As an aside you might want to join on the node table to only select published content, but that's the gist of it.