Magento Create New Filed For Categories

Create one php file into your App folder, write the below code in that file and run this file.
Then go to Catalog -> Manage Catagory and see there your custom fields.

<?php
//    initialize magento environment for 'default' store
    require_once 'app/Mage.php';
    Mage::app('default');

    echo "initialising";
    echo runAdd();
    echo "finishing";

function runAdd()
{
    $setup = new Mage_Eav_Model_Entity_Setup('core_setup');
    // below code will add text attribute
    $setup->addAttribute('catalog_category', 'short_description', array(
        'group'         => 'General',
        'input'         => 'textarea',
        'type'          => 'varchar',
        'label'         => 'Short Description',
        'backend'       => '',
        'visible'       => 1,
        'required'      => 0,
        'user_defined'  => 1,
        'global'        => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_GLOBAL,
    ));
}