Hey g1138,
The way I was taught, when rescuing an unconscious diver from depth (ie - not on the surface), as lamont stated, you "ride" the diver up to the surface (similar to how you could position yourself - straddling the tank - in a rescue of a panicked diver at the surface) controlling the ascent with their wing.
As stated by Sat Diver, you keep the airways open during this.
To answer your question, if the second stage is still in their mouth, you "cup" their chin with your palm and hold the regulator in place with the trigger and middle fingers, tilting their head slightly backwards and towards you (remember, you will be straddling their tank from the back at this point). If their regulator has fallen out of their mouths, don't bother trying to put it back in, just surface as quickly as you can while not endangering yourself.
Remember, the first thing about rescue is to ensure you do not put yourself in unnecessary danger.
As per your question about a DIR diver, if said diver is on anything other than singles, chances are they will have some deco requirements. In this case, there is not much you can do but surface the unconscious diver anyway. You can look at it this way: The diver is dead if you do nothing. You can't really make the situation any worse for said diver at this stage. Do the best you can, as you were trained. That's all anyone can expect.
Dive safe!