For this you need to create  following files as explained in the following example:
Example:
Company name: Coreover
Module Name:  Catalog

File path: app\code\local\Coreover\Catalog\etc\config.xml
Config.xml file:
<?xml version="1.0"?>
<config>
.............

    <global>
        <blocks>
            <catalog>
                <rewrite>
                    <product_list_toolbar>Coreover_Catalog_Block_Product_List_Toolbar</product_list_toolbar>
                </rewrite>
            </catalog>
        </blocks>
      ..............
    </global>
............
</config>


File Path: app\code\local\Coreover\Catalog\Block\Product\List\Toolbar.php

Php file for your module :

<?php
class Coreover_Catalog_Block_Product_List_Toolbar extends Mage_Catalog_Block_Product_List_Toolbar {

//Your Code for rewriting functions

}
?>