Dump file of your database created by phpMyAdmin or other tool, lets call it dump.sql. You can also use GZip compressed dump files, lets call it dump.gz.
Access account for your mySQL database
Access account for some web server with PHP and mySQLi installed. This web server must be able to connect to the mySQL database. This ability is probably present if your web server and the mySQL server are from the same ISP.
Some good text editor like Notepad++ to edit the configuration file.
Some FTP client to upload the files to the web server.
Common knowledge about files, PHP, mySQL databases, phpMyAdmin, FTP and HTTP