You can add static block to CMS page in Magento in following 2 ways:

1.) By adding code in Layout Update XML of CMS page:

<reference name="left">  
 <block name="block_name_anything" type="cms/block">  
 <action method="setBlockId">  
 <block_id>STATIC_BLOCK_ID_HERE</block_id>  
 </action>  
 </block>  
</reference>

2.) By putting below code directly into CMS Page content area:

 {{block type=”cms/block” block_id=”STATIC_BLOCK_ID_HERE”}}

Make sure you flush Blocks HTML Output cache if your changes do not reflect on website.