Add attributes for categories with installer

add_category_attribute.php

<?php

try {

    /** @var Mage_Catalog_Model_Resource_Setup $installer */
    $installer = $this;
    $installer->startSetup();

    $installer->addAttribute(
        Mage_Catalog_Model_Category::ENTITY,
        'my_custom_field',
        array(
            'group' => 'Display Settings', //it could be also "General Information","Custom Design"
            'type' => 'varchar',
            'label' => 'My Custom Label Field',
            'input' => 'text',
            'global' => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_GLOBAL,
            'required' => false,
            'visible_on_front' => false,
            'used_in_product_listing' => false,
            'sort_order' => 200,
            'note' => 'add comment here if you want'
        )
    )
    ->addAttribute(
        Mage_Catalog_Model_Category::ENTITY,
        'my_custom_select',
        array(
            'group' => 'General Information',
            'type' => 'text',
            'label' => 'My Custom Select Label',
            'input' => 'select',
            'frontend_class' => '',
            'source' => 'namespace_module/adminhtml_source_category_tree', // get your own adminhtml model
            'backend' => '',
            'frontend' => '',
            'global' => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_STORE,
            'required' => false,
            'visible_on_front' => false,
            'is_configurable' => false,
            'used_in_product_listing' => false,
            'sort_order' => 150,
            'note' => 'add comment here if you want'
        )
    );

} catch (Exception $e) {
    // Silence is golden
    Mage::logException($e);
    if (Mage::getIsDeveloperMode()) {
        Mage::throwException($e->getMessage());
    }
}