今回は特定のチャンネルで直近3ヶ月のランキングの取得方法です。
youtube APIキーの取得方法は割愛します。

<?php
  //取得側
  $PERIOD = date("Y-m-d",strtotime("-3 month")).'T00:00:00Z';
  $DEVELOPER_KEY = "XXXXXXXAPIキーXXXXXXX";
  $params = array(
      "type" => "video",
      "part" => "snippet",
      "maxResults" => 3,
      'regionCode' => 'JP',
      'channelId' => 'XXXXXXXチャンネルIDXXXXXXX',
      'order' => 'viewCount',
      'publishedAfter' => $PERIOD,
      "key" => $DEVELOPER_KEY,
  );
  $query = "";
  foreach ($params as $key => $value) {
    $query .= $key . "=" . $value . "&";
  }
  $query = substr($query, 0, -1);
  $url = "https://www.googleapis.com/youtube/v3/search?".$query;
  $result = file_get_contents($url);
  $result = json_decode($result);
  $rankingList = array();
  foreach ($result->items as $key => $value) {
    $rankingList[] = array(
      "videoId" => $value->id->videoId,
      "title" => $value->snippet->title,
      "description" => $value->snippet->description,
      "thumbnails_medium" => $value->snippet->thumbnails->medium->url,
    );
  }
?>
<?php 
  //出力側
  echo $rankingList[0]["videoId"];
  echo $rankingList[0]["title"];
  echo $rankingList[0]["description"];
  echo $rankingList[0]["thumbnails_medium"];
?>