I found an article that makes the task of replacing a stainless steel refrigerator door almost seem easy.
First, it says to wear gloves, so you don’t leave any kind of marks on the surface. The article assumes that the machine is unplugged, disconnected from the water supply, and that the old door is already off.
Second, position the door on the bottom hinge perpendicular to the body of the fridge. Make sure the front of the door lines up with the side of the fridge and lower the door straight down on the hinge pin.
Next, replace the top hinge. Snap on the hinge covers, if necessary.
Make sure it’s level. The article suggests eyballing it, but there’s nothing wrong with actually using a level, if convenient. Why not, eh? Make any adjustments until you are satisfied. You don’t want the door to be inadequately sealed.
Reconnect any wiring and water tubing (for any door with either an ice or water dispenser).
Finally, plug the fridge back in and reconnect it to the water supply. Turn the fridge on, and close the door. Voila.