your host will need to have PHP on their server.
This refers to the PHP script engine. You will not be able to install it on your host's server; they either provide it as a service or they don't. Ask 'em.
Another tutorial told that:
Often when setting up PHP scripts on web hosting accounts you will see the requirement to set some files and directories to chmod 777.
That is a Unix/Linux idea and relates to file permissions. 777 means that the owner of the file, the group owner, and everyone else, all have read, write and execute/change directory rights to the file or folder. There aren't many cases where you'd need to set such permissions, and it leaves a fairly glaring security hole since if anyone can change a script, they can run any (dangerous) program on your server...
Changing file/folder permissions is either done in your host's control panel, or through your FTP program, so it's impossible to give generic instructions.