<div>
    <div>Other Div</div><button>Click Me</button>
</div>
<div>
    <div>Other Div</div><button>Click Me</button>
</div>

var buttons = document.body.getElementsByTagName('button');
for(var x = 0; x < buttons.length; x++) {
    buttons[x].onclick = function() {
        this.previousSibling.style.backgroundColor = '#3a6d90';
    }
}
​