The trick to hanging wallpaper on a high staircase, according to Diyfixit, is to first build a stable platform to work from. (See References 1). After that, the technique is the same as for wallpapering more easily accessible places. Work away from the platform until reaching is difficult. Then reposition your platform as required to continue the work.
Follow the advice of Let’s do diy and open out the step ladder on the landing, a safe distance back from the edge. A step ladder is a type of ladder with a central hinge, which looks like an upside down V when opened out. Lock the ladder in place using the safety catch.
Set the straight ladder lower down, against the back of a step and the opposite wall, in line with the step ladder. Place the scaffolding boards between the two ladders. on rungs at the same height. Test the boards for stability before standing on them. You can now start wallpapering.
Use a spirit level to draw a straight line down the wall. Do this at the best start point, in terms of access and desired look. Measure the line. Cut a piece of wallpaper a few cms longer than this. Paste the back of the wallpaper. Stick it to the wall with one edge up to the line. Smooth it out.
Hold the roll up to the stuck piece to match the pattern correctly. Ensure the pattern match will allow enough paper at the top and bottom of the next section of wall. Cut the paper as before. You can trim off any excess when the paper has dried.
Proceed in like manner, butting each subsequent piece to the preceding one to maintain correct vertical positioning. For corners, fold the paper so it sits neatly on both planes. Make any adjustment cuts required to ensure the paper lies flat. Trim all the pieces to length when the paper has nearly dried.
Another option is a ladder leveller. Ladder levellers come in several different designs but basically, they extend one of the legs of the ladder so it can straddle two or more steps and stay level.
Wallpapering is usually easier with two people.
If you detect any instability while on your platform, dismount at once and reposition the scaffolding boards as required.