You need to create your own block, or at least one template.
Here is the short version using only a template.
Create the file app/design/frontend/base/default/template/homepage/categories.phtml with this content:
<?php
$rootId = Mage::app()->getStore()->getRootCategoryId();
$categories = Mage::getModel('catalog/category')->getCollection()
->addAttributeToSelect('*')
->addAttributeToFilter('parent_id', $rootId)
->setOrder('position')
->addAttributeToFilter('include_in_menu', 1) //this is needed if you want only the categories in the menu
->addAttributeToFilter('is_active', 1);
$_helper = $this->helper('catalog/output');
?>
<?php if ($categories->count() > 0) : ?>
<ul>
<?php foreach ($categories as $category) : ?>
<li>
<div class="name">
<a href="<?php echo $category->getUrl()?>" title="<?php echo $this->escapeHtml($category->getName())?>"><?php echo $category->getName()?></a>
</div>
<div class="image">
<?php if ($category->getImageUrl()) :?>
<img src="<?php echo $category->getImageUrl()?>" alt="<?php echo $this->escapeHtml($category->getName())?>" />
<?php endif;?>
</div>
<div class="description">
<?php echo $_helper->categoryAttribute($category, $category->getDescription(), 'description') ?>
</div>
</li>
<?php endforeach;?>
</ul>
<?php endif;?>
Now you need to add this to the homepage content:
{{block type="core/template" template="homepage/categories.phtml"}}
The markup of the template may need some modifications in order to make it a slider, but all the elements you need are there.
There is a cleaner method where you create you own block and move the code that retrieves the categories to a block method and call that method in the template. But the idea is the same.
I haven't tested the code so be careful at syntax errors.
=> Yeah syntax error was at line 5 and 25. Made correct it.
