MySql backup and recovery. please help!

So I have an important issue to deal with.
I need to move the sql database from one please to another, usually i just use phpMyAdmin but on this machine i don’t have such advanced features. Its a VPS by imarto, the MySQL options i have is to execute sql or to make a backup. the backup is a file with which i have no idea what to do and how to check it.

can anyone please help? moth time work depends on it… :confused::confused::confused::confused:

Oh and the backup file begins with this code

-- MySQL dump 10.13  Distrib 5.5.35, for debian-linux-gnu (i686)
--
-- Host: localhost    Database: sionclinic
-- ------------------------------------------------------
-- Server version	5.5.35-0+wheezy1

/*!40101 SET @OLD_CHARACTER_SET_CLIENT=@@CHARACTER_SET_CLIENT */;
/*!40101 SET @OLD_CHARACTER_SET_RESULTS=@@CHARACTER_SET_RESULTS */;
/*!40101 SET @OLD_COLLATION_CONNECTION=@@COLLATION_CONNECTION */;
/*!40101 SET NAMES utf8 */;
/*!40103 SET @OLD_TIME_ZONE=@@TIME_ZONE */;
/*!40103 SET TIME_ZONE='+00:00' */;
/*!40014 SET @OLD_UNIQUE_CHECKS=@@UNIQUE_CHECKS, UNIQUE_CHECKS=0 */;
/*!40014 SET @OLD_FOREIGN_KEY_CHECKS=@@FOREIGN_KEY_CHECKS, FOREIGN_KEY_CHECKS=0 */;
/*!40101 SET @OLD_SQL_MODE=@@SQL_MODE, SQL_MODE='NO_AUTO_VALUE_ON_ZERO' */;
/*!40111 SET @OLD_SQL_NOTES=@@SQL_NOTES, SQL_NOTES=0 */;

--
-- Table structure for table `nl_link_stats`
--

DROP TABLE IF EXISTS `nl_link_stats`;
/*!40101 SET @saved_cs_client     = @@character_set_client */;
/*!40101 SET character_set_client = utf8 */;
CREATE TABLE `nl_link_stats` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `key` varchar(255) NOT NULL,
  `keyword` varchar(255) NOT NULL,
  `occurrences` int(11) unsigned NOT NULL DEFAULT '0',
  `links_data` mediumtext,
  `domain` varchar(255) NOT NULL,
  PRIMARY KEY (`id`),
  FULLTEXT KEY `keyword_idx` (`keyword`),
  FULLTEXT KEY `link_data_idx` (`links_data`),
  FULLTEXT KEY `key_idx` (`key`)
) ENGINE=MyISAM AUTO_INCREMENT=848 DEFAULT CHARSET=utf8;
/*!40101 SET character_set_client = @saved_cs_client */;

mysql> source ‘full path of the backupfile’;