Like this:

var root = document.getElementsByTagName( 'html' )[0]; // '0' to assign the first (and only `HTML` tag)



root.setAttribute( 'class', 'myCssClass' );

Or use this as your 'setter' line to preserve any previously applied classes: (thanks @ama2)

root.className += ' myCssClass';

Or, depending on the required browser support, you can use the classList.add() method:

root.classList.add('myCssClass');

https://developer.mozilla.org/en-US/docs/Web/API/Element/classList
http://caniuse.com/#feat=classlist

UPDATE:

A more elegant solution for referencing the HTML element might be this:

var root = document.documentElement;

root.className += ' myCssClass';

// ... or:

//  root.classList.add('myCssClass');

//