<core-animated-pages> extends <core-selector>, and most of the "magic" about selecting what's shown is delegated to <core-selector>.
There are a few different ways of triggering a selection change with something that extends <core-selector>. The most relevant when talking about <core-animated-pages> is either binding to the selected= attribute and changing that value (in the case of <core-animated-pages>, it takes a numeric index of the page to select, starting with 0), or using the selectPrevious()/selectNext() methods.
There's a pretty thorough rundown of navigating between <core-animated-pages> in the "Building single page apps using web components" article. But if you want something quick to hack around with, try this:
<!doctype html>
<html>
<head>
<meta charset="utf-8">
<title>Polymer Demo</title>
</head>
<body>
<script src="//www.polymer-project.org/webcomponents.min.js"></script>
<link rel="import" href="//www.polymer-project.org/components/core-animated-pages/core-animated-pages.html">
<polymer-element name="sample-element">
<template>
<div>
<button on-tap="{{previousPage}}">Previous</button>
Page <input value="{{selectedPageIndex}}"> (0-indexed)
<button on-tap="{{nextPage}}">Next</button>
</div>
<core-animated-pages id="pages"
selected="{{selectedPageIndex}}">
<section>
<h1>First Page</h1>
<p>Hello!</p>
</section>
<section>
<h1>Second Page</h1>
<p>Hi!</p>
</section>
<section>
<h1>Third Page</h1>
<p>Howdy!</p>
</section>
</core-animated-pages>
</template>
<script>
Polymer({
selectedPageIndex: 0,
previousPage: function() {
this.$.pages.selectPrevious(true);
},
nextPage: function() {
this.$.pages.selectNext(true);
}
});
</script>
</polymer-element>
<sample-element></sample-element>
</body>
</html>