Mike, if there is padding under the carpet, the carpet is stretched onto tack strip, which runs continuously near all the walls, at the back edge of each tread (the horizontal surfaces) and at the bottom of each riser (the vertical surfaces).
The stairs will usually be a number of steps all from one piece of carpeting, but some can be individual steps, too. Since this is a 90º landing it should be a separate piece from the step above it.
Beginning at the corner where the wall turns (the outer-most corner, away from the steps) you can begin pulling the carpet up from the tack strip. Grab the yarn in the corner with pliers to get a start if needed. Use caution with your hands around tack strip; it can rip you up pretty good. In pulling the carpet loose, pull upwards in line with the wall, not "peeling it back"; the tacks in tack strip are angled towards the wall to keep a hold on the carpet.
You should be able to pull up the two wall sides, and the edge which meets the ascending riser. Once this is done, check where the landing carpet descends the first riser; from one side try to pull it off the tack strip at the bottom of the riser. If it is connected to the next stair tread, stop, and fold the landing carpet backwards to do the repair needed. If it's a separate piece, you can remove it from the stairway and set aside until the repair is done.
NOTE: Children beware around exposed tack strip! Don't let them near it.
Once your floor repair is done, have the landing carpet re-installed by a carpet installer who can properly re-stretch it.