When you are customize the magento site you may be want to get current category,root category and sub category details like category ID,name,…etc.Here is a simple example.
// Load libraries
$layer = Mage::getSingleton('catalog/layer');
$_category = $layer->getCurrentCategory();
// Get Current category ID
$currentCategoryId = $_category->getId();
//Get current category all details
$current_category = Mage::registry('current_category');
// Get Parent category ID of the current category like root category
$parent_id = $current_category->parent_id;
If you want to load known category details ,for a example want to load category id=10, details.That is like this.
$_category = Mage::getModel('catalog/category')->load(10); // category ID=10
echo $_category->getUrl(); // get category URL
echo $_category->getUrlKey(); // get category URL Key
echo $_category->getName(); // get category Name