Open CMS->Pages->[your page] in Magento Admin Panel.
Add the following layout instructions to Design tab->Page Layout->Layout Update XML
<block type="catalog/product_list" name="product_list"
template="catalog/product/list.phtml">
<action method="setCategoryId"><category_id>3</category_id></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>empty</layout>
<count>6</count>
</action>
<action method="addColumnCountLayoutDepend">
<layout>one_column</layout>
<count>5</count>
</action>
<action method="addColumnCountLayoutDepend">
<layout>two_columns_left</layout>
<count>4</count>
</action>
<action method="addColumnCountLayoutDepend">
<layout>two_columns_right</layout>
<count>4</count>
</action>
<action method="addColumnCountLayoutDepend">
<layout>three_columns</layout>
<count>3</count>
</action>
<action method="setToolbarBlockName"><name>product_list_toolbar</name></action>
</block>
<block type="catalog/layer_view" name="cms_layer" as="cms_layer" before="-">
<action method="setCategoryId"><category_id>3</category_id></action>
</block>
Also insert ID of desired category in 3 (2 times).
Open desired category of your store through Catalog->Manage Categories. Make sure that Is Anchor=Yes on Display Settings tab.