Measure the doorways and corners of the stairway through which you are moving the desk and compare those measurements to the desk. This helps you determine whether the desk fits through the stairway at all.
Remove all the drawers. Drawers can slip out and break when you are moving the desk. Removing the drawers also makes the desk substantially lighter.
Remove the desk's feet if they can be removed. Reducing the height of the desk can make the desk go around corners and through narrow doorways a little easier.
Use furniture lifting straps to carry the desk. Furniture straps are simply straps made of sturdy webbing that you can loop underneath the desk. This prevents you from needing to bend down to pick up the desk and it also prevents you from needing to carry the desk while you are hunched over.
Turn the desk on its side and hook two of the legs around the corner if the desk has an open back. This can help when maneuvering the desk around a tight doorway or corner.