You would have to drop a list below the button, in a manner similar to the demo provided here for autocomplete: http://jqueryui.com/demos/autocomplete/.
Essentially, you would replace the code in the button demo that displays the alert "could display a menu with a selected action" with code that does just that. This code can fire off one of the many jQuery Menu plugins out there, like this one.
<div class="demo">
<div>
<button id="rerun">Run last action</button>
<button id="select">Select an action</button>
</div>
</div>
<script type="text/javascript">
$(function() {
$("#rerun").button().click(function() {
alert("Running the last action");
})
.next()
.button({
text: false,
icons: {
primary: "ui-icon-triangle-1-s"
}
})
.click(function() {
// Code to display menu goes here. <<<<<<<<<<<<
})
.parent()
.buttonset();
});