Here, how to add new action in grid like ‘Edit’ link at admin grid.
On this example, we will add a “schedule” action in product admin grid.

We will overrite this class /app/code/core/Mage/Adminhtml/Block/Catalog/Product/Grid.php.

Declare the rewrite class on the /app/code/local/Adin/Catalog/etc/config.xml
and add

<global>
      <blocks>
            <adminhtml>
                <rewrite>
                    <catalog_product_grid>Adin_Catalog_Block_Adminhtml_Catalog_Product_Grid</catalog_product_grid>
                </rewrite>
            </adminhtml>
        </blocks>
</global>

Then create your rewritted class /app/code/local/Adin/Catalog/Block/Adminhtml/Catalog/Product/Grid.php.

<?php
class Adin_Catalog_Block_Adminhtml_Catalog_Product_Grid extends Mage_Adminhtml_Block_Catalog_Product_Grid {
}
?>

Now, rewrite the _prepareColumns() function, find the ‘action’ column an add an entry in the actions array

  $this->addColumn('action',
            array(
                'header'    => Mage::helper('catalog')->__('Action'),
                'width'     => '50px',
                'type'      => 'action',
                'getter'     => 'getId',
                'actions'   => array(
                    array(
                        'caption' => Mage::helper('catalog')->__('Edit'),
                        'url'     => array(
                            'base'=>'*/*/edit',
                            'params'=>array('store'=>$this->getRequest()->getParam('store'))
                        ),
                        'field'   => 'id'
                    ),
                    array(
                        'caption' => Mage::helper('catalog')->__('Schedule'),
                        'url'     => array(
                            'base'=>'*/*/schedule',
                            'params'=>array('store'=>$this->getRequest()->getParam('store'))
                        ),
                        'field'   => 'id'
                    ),
                ),
                'filter'    => false,
                'sortable'  => false,
                'index'     => 'stores',
            ));

In our example, we just add this part

array(
                        'caption' => Mage::helper('catalog')->__('Schedule'),
                        'url'     => array(
                            'base'=>'*/*/schedule',
                            'params'=>array('store'=>$this->getRequest()->getParam('store'))
                        ),
                        'field'   => 'id'
                    ),

One last thing, at the end of the _prepareColumns function, change

return parent::_prepareColumns();

by

return Mage_Adminhtml_Block_Widget_Grid::_prepareColumns();