Instructions
Approach the staircase from the direction it's facing. If the staircase ascends to the left, then approach it from the right. If it ascends to the right, approach it from the left.
Push the "Up" arrow while still approaching the staircase and Jackson will climb the staircase. He'll walk by the stairs If you do not hold the "Up" arrow.
Continue walking in the direction in which the staircase ascends. Jackson will eventually reach the top the stairs, at which point you can let go of the "Up" arrow.