Following the documentation of the YUI DataTable control i've inferred the following code:
<!DOCTYPE HTML>
<HTML>
<HEAD>
<SCRIPT type="text/javascript" src="http://yui.yahooapis.com/3.5.1/build/yui/yui-min.js"></SCRIPT>
<SCRIPT type="text/javascript">
// Create a new YUI instance and populate it with the required modules.
YUI().use('datatable', function (Y) {
// Columns must match data object property names
var data = [
{ id: "ga-3475", name: "gadget", price: "$6.99", cost: "$5.99" },
{ id: "sp-9980", name: "sprocket", price: "$3.75", cost: "$3.25" },
{ id: "wi-0650", name: "widget", price: "$4.25", cost: "$3.75" }
];
var table = new Y.DataTable({
columns: ["id", "name", "price"],
data: data,
// Optionally configure your table with a caption
caption: "My first DataTable!",
// and/or a summary (table attribute)
summary: "Example DataTable showing basic instantiation configuration"
});
table.render("#example");
});
</SCRIPT>
</HEAD>
<BODY>
</BODY>
</HTML>
The insulting thing is that the documentation says:
This code produces this table:
except that this code produces this table:

So obviously i'm missing something pretty fundamental about how to render a YUI data table. What is the correct way to render a YUI data table?
Q. How to render a YUI datatable?
Another page mentions including a <div>, changing my <BODY> from empty to:
<BODY>
<div class="example yui3-skin-sam">
<div id="simple"></div>
<div id="labels"></div>
</div>
</BODY>
but does not change the look of the control.

Move the <script>s to the bottom of the <body>, or at least after the <div> that will contain the DataTable. That will avoid a race condition where the scripts may be loaded before the DOM is set up.
render('#example') is telling the DataTable to render into an element with an id of 'example' The markup sample you included has a div with a class of 'example', then two divs with ids 'simple' and 'labels'. You need to make sure you're rendering inside a parent element with class yui3-skin-sam. If you tell a YUI widget to render into an element it can't find, it falls back to rendering it inside the <body>. You can fix this in a few ways:
In any case, make sure your render target is inside an element with class="yui3-skin-sam"