I've ridden up and down stairs a bit on my WR250X supermoto and here's some things I've found that work for me...
When going up stairs, it's different from going up a hill of the same incline. I have to lean way back to keep the front wheel from digging into the edge of the step. So lean back and let that front wheel come up. You also have to stay on the throttle. If you chop the throttle the forks will dive and you'll bottom out or stall out.
Going down stairs is simple. Just like going down a steep hill, you keep your weight back and use the back brake to slow your speed.