By iterating over the elements, and checking if it matches.

Generic code that finds the index of the element within it's parents childNodes collection.

function index(el) {

    var children = el.parentNode.childNodes,

        i = 0;

    for (; i < children.length; i++) {

        if (children[i] == el) {

            return i;

        }

    }

    return -1;

}

Usage:

// should return 4

var idx = index(document.body.childNodes[4]);

EDIT: I can't delete an accepted answer, but @kennebec's answer below is much better, which I'll quote verbatim:

You can use Array.prototype.indexOf.call() like this

let nodes = document.getElementsByTagName('*');

Array.prototype.indexOf.call(nodes, document.body);