How to add new or customize existing top header links in Magento?

@tbiinfotech this code works

<default><reference name="top.links"><action method="addLink" translate="label title"><label>Terms and Condition</label><url>terms</url>
<title>Terms and Condition</title><prepare>true</prepare>
<position>2</position> </action></reference></default>

How do we add the store ID if we are running a multistore with a common theme?

Top-links are managed in magento through layout xml files.

To add a link to top links, we need to add xml code to layout files

Adding More Links To The Top Links. -

Suppose we need to add a new link to top links, lets say a link for a CMS page called Terms and Conditions.

To do this open a layout file, let say customer.xml and add the below code:

<default>
<reference name="top.links">
  <action method="addLink" translate="label title">
    <label>Terms and Condition</label>
    <url>terms</url>
    <title>Terms and Condition</title>
    <prepare>true</prepare>
    <position>2</position>
  </action>
</reference>
</default>

This code should a new link to top links.

You should create a block in

app/design/frontend/package/theme/newheader/new_header.phtml 

in new_header.phtml you put what you want icones, texts etc...

then in app/design/frontend/package/theme/layout/local.xml and put this:

<reference name="header">
   <block type="core/template" name="new.header" template="newheader/new_header.phtml"/>
</reference>

<block type="page/template_links" name="top.links" as="topLinks">
 <action method="addLink" translate="label title">
   <label>Blog</label>
   <url>/blog</url>
   <title>Blog</title>
   <prepare/>
   <urlParams/>
   <position>1</position>
   <liParams>class-name</liParams>
   <aParams></aParams>
 </action>
</block>

place above code in app/design/front/[Your-Package]/[Your-Theme]/layout/local.xml in <default></default> element.

Style it using "class-name"