Magento: New Product in home page with pagination

app/code/local/Mage/Catalog/Block/Product/New.php

<?php
class Mage_Catalog_Block_Product_New extends Mage_Catalog_Block_Product_List
{
    function get_prod_count()
    {
        //unset any saved limits
        Mage::getSingleton('catalog/session')->unsLimitPage();
        return (isset($_REQUEST['limit'])) ? intval($_REQUEST['limit']) : 10;
    }// get_prod_count

    function get_cur_page()
    {
        return (isset($_REQUEST['p'])) ? intval($_REQUEST['p']) : 1;
    }// get_cur_page

    /**
     * Retrieve loaded category collection
     *
     * @return Mage_Eav_Model_Entity_Collection_Abstract
     **/
    protected function _getProductCollection()
    {
        $todayDate  = Mage::app()->getLocale()->date()->toString(Varien_Date::DATETIME_INTERNAL_FORMAT);

        $collection = Mage::getResourceModel('catalog/product_collection');
        $collection->setVisibility(Mage::getSingleton('catalog/product_visibility')->getVisibleInCatalogIds());

        $order = (isset($_REQUEST['order'])) ? $_REQUEST['order'] : "name";
        $dir = (isset($_REQUEST['dir'])) ? $_REQUEST['dir'] : "asc";

        $collection = $this->_addProductAttributesAndPrices($collection)
            ->addStoreFilter()
            ->addAttributeToFilter('news_from_date', array('date' => true, 'to' => $todayDate))
            ->addAttributeToFilter('news_to_date', array('or'=> array(
                0 => array('date' => true, 'from' => $todayDate),
                1 => array('is' => new Zend_Db_Expr('null')))
            ), 'left')
            ->addAttributeToSort($order, $dir)
            ->setPageSize($this->get_prod_count());

        $collection->setCurPage($this->get_cur_page());
        $this->setProductCollection($collection);
        return $collection;
    }// get product collection
}
?>

app->design->fronted->your_package->your_theme->template->catalog->product->new.phtml

<?php
$_productCollection=$this->getProductCollection();
$_helper = $this->helper('catalog/output');
?>
<?php if(!$_productCollection->count()): ?>
    <p class="note-msg"><?php echo $this->__('There are no products matching the selection.') ?></p>
<?php else: ?>
    <div class="category-products">
        <?php echo $this->getToolbarHtml() ?>
        <?php // List mode ?>
        <?php if($this->getMode()!='grid'): ?>
            <?php $_iterator = 0; ?>
            <ol class="products-list" id="products-list">
                <?php foreach ($_productCollection as $_product): ?>
                    <li class="item<?php if( ++$_iterator == sizeof($_productCollection) ): ?> last<?php endif; ?>">
                        <?php // Product Image ?>
                        <a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" class="product-image"><img src="<?php echo $this->helper('catalog/image')->init($_product, 'small_image')->resize(135); ?>" width="135" height="135" alt="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" /></a>
                        <?php // Product description ?>
                        <div class="product-shop">
                            <div class="f-fix">
                                <?php $_productNameStripped = $this->stripTags($_product->getName(), null, true); ?>
                                <h2 class="product-name"><a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $_productNameStripped; ?>"><?php echo $this->htmlEscape($_product->getName()) ?></a></h2>
                                <div class="desc std">
                                    <?php echo $_helper->productAttribute($_product, $_product->getShortDescription(), 'short_description') ?>
                                    <a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $_productNameStripped ?>" class="link-learn"><?php echo $this->__('Learn More') ?></a>
                                </div>
                                <?php echo $this->getPriceHtml($_product, true) ?>
                                <?php if($_product->isSaleable()): ?>
                                    <p><button type="button" title="<?php echo $this->__('Add to Cart') ?>" class="button btn-cart" onclick="setLocation('<?php echo $this->getAddToCartUrl($_product) ?>')"><img src="<?php echo $this->getSkinUrl('images/add_to_cart_btn.gif');?>"/></button></p>
                                <?php else: ?>
                                    <p class="availability out-of-stock"><span><?php echo $this->__('Out of stock') ?></span></p>
                                <?php endif; ?>
                                <?php echo $this->getReviewsSummaryHtml($_product, 'short') ?>
                            </div>
                        </div>
                    </li>
                <?php endforeach; ?>
            </ol>
            <script type="text/javascript">decorateList('products-list', 'none-recursive')</script>

        <?php else: ?>

            <?php // Grid Mode ?>

            <?php $_collectionSize = $_productCollection->count() ?>
            <?php $_columnCount = $this->getColumnCount(); ?>
            <?php $i=0; foreach ($_productCollection as $_product): ?>
            <?php if ($i++%$_columnCount==0): ?>
            <ul class="products-grid">
        <?php endif ?>
            <li class="item<?php if(($i-1)%$_columnCount==0): ?> first<?php elseif($i%$_columnCount==0): ?> last<?php endif; ?>">
                <a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" class="product-image"><img src="<?php echo $this->helper('catalog/image')->init($_product, 'small_image')->resize(135); ?>" width="135" height="135" alt="<?php echo $this->stripTags($this->getImageLabel($_product, 'small_image'), null, true) ?>" /></a>
                <h2 class="product-name">
                    <a href="<?php echo $_product->getProductUrl() ?>" title="<?php echo $this->stripTags($_product->getName(), null, true) ?>">
                        <?php echo $this->htmlEscape($_product->getName()) ?>
                    </a>
                </h2>
                <?php echo $this->getReviewsSummaryHtml($_product, 'short') ?>
                <?php echo $this->getPriceHtml($_product, true) ?>
                <div class="actions">
                    <?php if($_product->isSaleable()): ?>
                        <button type="button" title="<?php echo $this->__('Add to Cart') ?>" class="button btn-cart" onclick="setLocation('<?php echo $this->getAddToCartUrl($_product) ?>')"><img src="<?php echo $this->getSkinUrl('images/add_to_cart_btn.gif');?>"/></button>
                    <?php else: ?>
                        <p class="availability out-of-stock"><span><?php echo $this->__('Out of stock') ?></span></p>
                    <?php endif; ?>
                </div>
            </li>
            <?php if ($i%$_columnCount==0 || $i==$_collectionSize): ?>
            </ul>
        <?php endif ?>
        <?php endforeach ?>
            <script type="text/javascript">decorateGeneric($$('ul.products-grid'), ['odd','even','first','last'])</script>
        <?php endif; ?>

        <div class="toolbar-bottom">
            <?php echo $this->getToolbarHtml() ?>
        </div>
    </div>
<?php endif; ?>

Add code in cms->page->design->Layout Update XML area.

<reference name="content">
    <block type="catalog/product_new" name="product_new" template="catalog/product/new.phtml">
        <action method="setCategoryId"><category_id>4</category_id></action>
        <action method="setColumnCount"><column_count>3</column_count></action>
        <action method="setProductsCount"><count>0</count></action>
        <block type="catalog/product_list_toolbar" name="product_list_toolbar" template="catalog/product/list/toolbar.phtml">
            <block type="page/html_pager" name="product_list_toolbar_pager" />
        </block>
        <action method="addColumnCountLayoutDepend"><layout>one_column</layout><count>6</count></action>
        <action method="setToolbarBlockName"><name>product_list_toolbar</name></action>
    </block>
</reference>