Stairs are a good way to get to a higher floor. Their only problem, everything that walks, crawls, or generally moves on things that aren't wheels can use them. This includes zombies, so spare yourself the risk of the possibility of getting attacked while your sleeping or otherwise preoccupied by destroying the stairs.
Preparation[]
The idea is fairly simple. All you have to do is make the stairs "unusable." Obtain sledgehammers or axes to do the job. Other tools like hammers, chisels, and crowbars may help for certain situations. In certain settings, large vehicles may be able expediate the destruction, however, this will likely take a toll on the vehicle as well, shortening its lifespan. In any event, the more people and forethought, the more quickly the work will be done, and the less strained muscles will be.
Before starting the demolition, make sure that all of your supplies other than what you will use to destroy the stairs are on the upper level. Having someone at the top who can lower, or catch supplies is also a good idea. Ropes or tied sheets, curtains, or other fabrics can make for good improvised cranes.
Stairs that leave nothing behind are vastly preferable to stairs with solid material under them. Destruction of the steps in the red and green rectangles may still leave behind materials that zombies can crawl through. The yellow rectangle leaves only a gap to drop through. If your staircase is like the one in the red rectangle, you may still need to barricade after the stairs are gone.
Demolition[]
Ok, so you've obtained a sledgehammer or axe, moved your supplies onto the second floor, and you have a ladder. Now it's destruction time. Start from the bottom up. Don't stand on the stairs, so this should just be common sense. Do not use fire to demolish the stairs, as this may cause more damage than intended.
Aftermath[]
If done correctly, the result should a clearing that is difficult, if not impossible, to climb. If a ramp is created, a gap where there the zombie simply has nothing to grasp, or would have to lift himself off the ground will guard itself.
There are many things to do after that though. First, clear the area underneath where your stairs used to be. These things can be used as extra fortifications or for repairs, should it be necessary. Second, try to remove climbable debris or dead bodies from the location where the stairs were.
References[]
The Zombie Survival and Defense Wiki[1]