To transfer your website to another server follow these steps.

1. Backup your Database first using the admin panel of magento.
2. Create a new database in your new Server.
3. import your backup data to the new database.
4. upload a fresh copy of magento to your root directory.
5. copy the codes of your current magento website into the fresh magento directory. ( this will overwrite all of the affected codes ).
6. install magento (like how you normally install).
7. You should thank Engr. Julius Bacosa for this. Good Luck!!!