Several way you can move server, one of the most easiest way.
Follow the below Step:
1) Back up the files in the server
2) Export the Databse
3) Move the files to the new server
4) Import the databse to the new server
5) Edit the database details . please update the file “app/etc/local.xml”, with the latest Database details
6) Modify the table core_config_data (Replace old server name with new one).
7) Delete the files in “var/session” and “/var/cache”