I have not taken the door off of this vehicle, but I have off a few others. Generally you start by removing screws from outside around the door panel. You also have to remove the screw that holds on the plastic piece for the door handle. Sometimes the screws are covered by plastic pieces. I can take a look later and locate the screw locations. There are also some plastic pieces that must be popped out that hold on the door.
Does your model have power windows?
Someone a while ago posted some nice pictures of the doors with the panels removed. Unfortunately he deleted them from his photobucket account, so I uploaded two that I managed to save. Hopefully this helps.
This is in the section 'SF DIY and Our Little Workshop'
It appears this is for a 2007-2009 Santa Fa..looks like you have a 2010...might help?..not sure how similar they are...
BTW, 'TrackerS888' has another good post on replacing the stereo..removing part of dash/cover (again looks to be for a 2007-2009 Santa Fe)
see thread 'Sequence of Front Panel Removal - How to DIY version'