Please follow these steps:

1.Make a backup of moodle software directoty and moodledata folder.

2. Take a backup of the database using the below command:

    mysqldump -u username -p passwd database_name > filename.sql

3.create database on the new server by using create database query and   grant all the privilege given in installation documentation in moodle.org site.

4.Restore the backed up database using the below command:

mysql -u username -p passwd new_database_name < filename.sql

5.Poste your moodle folder  and moodledata folder in their respective directories.

6.Go to the url of your site and visit admin page and complete the setup.

If everything is restored correctly you will get successfully upgraded message.

All the best!