[javascript] How to use JavaScript to change div backgroundColor

Access the element you want to change via the DOM, for example with document.getElementById() or via this in your event handler, and change the style in that element:

document.getElementById("MyHeader").style.backgroundColor='red';

EDIT

You can use getElementsByTagName too, (untested) example:

function colorElementAndH2(elem, colorElem, colorH2) {
    // change element background color
    elem.style.backgroundColor = colorElem;
    // color first contained h2
    var h2s = elem.getElementsByTagName("h2");
    if (h2s.length > 0)
    {
        hs2[0].style.backgroundColor = colorH2;
    }
}

// add event handlers when complete document has been loaded
window.onload = function() {
    // add to _all_ divs (not sure if this is what you want though)
    var elems = document.getElementsByTagName("div");
    for(i = 0; i < elems.length; ++i)
    {
        elems[i].onmouseover = function() { colorElementAndH2(this, 'red', 'blue'); }
        elems[i].onmouseout = function() { colorElementAndH2(this, 'transparent', 'transparent'); }
    }
}