Magento has a good amount of template overriding methods. As per the Magento documentation, we will follow the standard method. Instead of editing core files we will use local.xml located in our custom
Adding the below line in to the header section of local.xml find in app/design/frontend/[your-package]/[your-theme]/layout/
After adding above code the header section will look like
Pasting the below code to header.phtml for displaying the store switcher lcoated in app/design/frontend/[your-package]/[your-theme]/template/page/html
<?php echo $this->getChildHtml('store_switcher')?>
You are there. Clear cache and check the page.