What does a novice DIY'er need to know before building a wall higher than 8' (14.5' feet to be exact)?
The right way to do this is to deconstruct the side and top of the stairway wall - remove the drywall, the stair railing, and the top plate for that wall, and then add additional studs. 

Your two choices are balloon framing that runs all the way to the ceiling and platform framing that is two separate walls stacked on top of each other. For platform framing, you would need to tie the top/bottom plates to the left and right walls so it would not move. Balloon framing would avoid this, so that would be my choice. Make sure to put proper fire blocking in. The stairs may be hung on the current wall, so you will want to make sure you don't mess up the current wall's structure. You can do this by sistering the new studs next to the old ones. 

This is a pretty straightforward thing to do. 

I would not recommend adding a full wall next to the existing wall; you would have to modify the floor covering and extend any utilities out to the surface of the new wall.