How you attach the stair stringers to the top of the deck and to any landings will be critical.   You should reinforce the rim behind the stairs to provide a solid base for attachment.  Use positive connections to install stair stringers using joist hangers or angled brackets to the front face to provide adaquate support. 

If your first tread steps down from the deck you must extend the rim joist to create a solid surface below the deck rim to attach to.  You should attach a 2x6 or 2x8 under the rim flush to the bottom of the stringer using strap ties or bolted cleats for added strength.  You may also want to use metal strap ties that can bend along the bottom of the stringer and over the top of the rim joist for added support.

Attaching to the top of a landing offers a similar situation in which you should always maintain a solid face connection.