This is a question that gets asked a lot by people who has just started out using Joomla.
There is different ways to do this but my personal preference is to use Akeeba backup and kickstart to restore your site on a new server.
Please watch the video bellow for a tutorial on how to restore your Joomla site on your server.
Option 1. Akeeba Kickstart
Option 2. Do a manual backup.
1. Copy entire site files and folder structure to new server using FTP.
2. Use phpmwyadmin to export the SQL database on your old server.
3. Use phpmyadmin to import SQL to new database on your new server.
4. Modify configuration.php to include hosts, database,user,password using an editor.
5. In backend of Joomla, use configuration to modify location of logfiles and temp
There may be some third party components or extensions that requires additional editing if you don’t know how to do this uninstall and reinstall. I have done this with dozens of sites. Good luck.
Please let me know if you need any help in the comments section bellow.