Who opens an airliner's door first after it lands?
It depends on the type of aircraft. But USA today/Ask the Captain gives a nice explanation:


  Question: I was wondering what takes so long to get the exit door open after we land. Could you please go through the steps?
  
  
  
  Answer: Once the airplane arrives at the gate and is properly chocked, the captain shuts down the engines and switches off the “Fasten Seat Belt” light. The anti-collision light (this is the red blinking light on the top and bottom of the airplane) is switched off, informing ground crew that it is safe to approach the airplane.
  
  Ground crew members then begin to position the jet bridge, aligning it with the door.  Once the jet bridge is mated to the aircraft and the cover is in place, the ground agent either opens the door or taps on it for the flight attendant to open it. This varies depending on the type of airplane to minimize the chance for an inadvertent slide deployment.
  
  Once the door is initially opened, the ground agent assists in fully opening it and ensuring that it is locked in the open position.
  
  This is the generic procedure for most jet airliners. Regional or smaller airplanes have a slightly different procedure as their stairs are built into the door.