Setting the system to parse html files as php is as simple as adding this line to your .htaccess file.
AddType application/x-httpd-php .html
If you don't have an .htaccess file at present, simply create one in a good text editor and upload it to the root of the account.
Yes, the period belongs there, and No, there is no file extension.
Some systems will not allow you to see or save the file without an extension on the file (Mac). Simply save it as a .txt file, upload and rename the file.