1- By Using Widget:

Step 1 : Go to Admin ->CMS->Pages->Home Page

Step 2 : Go to-> Home Page-> Content

Step 3 : Click to Show /HideEditor

Step 4 : Click on InsertWidget…

Step 5 : Choose “Widget Type”  Catalog New Product List

 Step 6: Fill up The Widget options as you want

 Step 7: Click on InsertWidget Top right of popup.

 Step 8: Save The Home Page and Clean your cache.

2- By Using Content Code:

Step 1 : Go to Admin ->CMS->Pages->Home Page

Step 2 : Go to-> Home Page-> Content

Step 3 :Copy and Pase the following code in content section.

{{block type="catalog/product_new" column_count="4" products_count="4" name="home.catalog.product.new" alias="products_homepage" template="catalog/product/new.phtml"}}

3- By Using XML Code:

Step 1 : Go to Admin ->CMS->Pages->Home Page

Step 2 : Go to-> Home Page-> Design

Step 3 :Copy and Pase the following code in Layout Update XML

<block type="catalog/product_new" name="home.catalog.product.new" alias="product_new" template="catalog/product/new.phtml" after="cms_page">
    <action  method="setColumnCount"><column_count>6</column_count></action>
    <action  method="setProductsCount"><count>3</count></action>
    <action method="addPriceBlockType">
        <type>bundle</type>
        <block>bundle/catalog_product_price</block>
        <template>bundle/catalog/product/price.phtml</template>
    </action>
</block>