Hi, if you are looking to grab all of the categories in your site and order them by the date they were created then you can use something along the lines of:
$categoryCollection = Mage::getModel('catalog/category')
->getCollection()
->addAttributeToSelect('*')
->setOrder('created_at', 'DESC')
->load();
You will probably want to replace ->addAttributeToSelect('*') by explicitly stating the attributes you want back - just to speed things up a little.
I have used DESC here as per your request but you could also use ASC for the opposite effect.
The code above will give you a whole collection. To get to the actual categories you will need to iterate over that collection with something like the following:
foreach($categoryCollection as $category) {
echo($category->getCreatedAt() . "<br/>");
}
This should give you a nicely printed out list of dates that each category was created.
To get more info on each category you can use things like $category->getName(), $category->getId() and so on. You get the idea.
This code will more than likely go in your block or helper and you can wrap it in a function which you will be able to call from your template to get access to the required category information.
Hopefully this helps.