$orderid = 12345;
$order = Mage::getModel('sales/order')->load($orderid);

The above code is roughly analogous to the following SQL query.

select * from sales_flat_order where entity_id=12345;

$incrementid = 100000000;
$order = Mage::getModel('sales/order')->loadByIncrementId($incrementid);

The above code is roughly analogous to the following SQL query.

select * from sales_flat_order where increment_id=100000000;

The increment_id is the customer facing order identifier, whereas the entity_id is the database level identifier for the order.

You can add comment and status to order. Get order :

$orderid = 12345;
$order = Mage::getModel('sales/order')->load($orderid);

And add comment:

//$isNotify means you want to notify customer or not.

$order->addStatusToHistory($status, $message, $isNotify);
$order->save()