Magento Category Navigation or Vertical category menu in sidebar

Here are the steps to retrive the category in the sidenbar
Step1. PHP Code to retrieve top level categories for navigation and save it at the following location.
in short this file contain code related to catalog Navigation Model which retrieves top level categories and show it in proper manner
Magento\app\design\frontend\base\default\template\catalog\navigation\categorymenu.phtml

<?php

/**
 * Left Category menu for store
 * We are showing  jsut the top level categorioes
 * @see Mage_Catalog_Block_Navigation
 */
?>
<div class="block block-category">
	<div class="inside-box">
		<div class="block-title block-category-title">
			<h3><?php echo $this->__('Our Categories') ?></h3>
		</div>
		<div class="block-category-navigation">
			<ul id="category-nav">
			<?php foreach ($this->getStoreCategories() as $_category): ?>
			<?php if($_category->name!=""):  ?>
				<li><?php echo $this->drawItem($_category) ?></li>
				<?php endif?>
				<?php endforeach ?>
			</ul>
		</div>
	</div>
</div>

Step2. Change the page.xml to include category navigation menu.

So let’s start with the home page, as in most of the cases. Magento home page is simple CMS page, therefore, we have to locate the page related layout XML file . that exists in our layout folder of selected theme. We are taking example as the default theme. So have to open the following file:

<block type="catalog/navigation" name="catalog.categorymenu" after="top.search" template="catalog/navigation/categorymenu.phtml"/>
Source : http://www.time2php.com/magento/magento-category-navigation-or-vertical-category-menu-in-sidebar