First you should create a backup of your database and code files. If you have Cpanel installed on your server, you can easily do that via Backups or Backup Wizard section. If you don't have Cpanel installed on your server, you should download all code files via FTP.
To create database backup you should access your database via phpMyAdmin. Select the database you want to create a backup of and go to Export section. Click 'Go' and that would download your database backup in SQL format.

On a new server you should create a database. For your convenience use the same database name and user you had on the old server.
Once database is created, access it via phpMyAdmin and navigate to the Import section. Select the database backup file you previously created in SQL format and click 'Go'. That would paste all data from your old database to the new one.

Upload all files from the old server to the new one either via FTP or create an archive with all your data and upload it via Cpanel File Manager. First option would require more time and good Internet connection.
Check your ow_includes/config.php file to make sure all information there is valid:

define('OW_URL_HOME', 'http://ow/'); //new site URL
define('OW_DB_HOST', 'localhost');         //new database host
define('OW_DB_PORT', null);                //new database port
define('OW_DB_USER', 'root');              //new database user
define('OW_DB_PASSWORD', '1234');          //new database password
define('OW_DB_NAME', 'ow');                //new database name

define('OW_PASSWORD_SALT', '4eca29633fc77');

Make following folders writable by setting 777 permissions:

ow_pluginfiles
ow_userfiles,
ow_static,
ow_smarty/template_c