The devices that you get to play with and use to complete puzzles in The Legend of Zelda: Tears of the Kingdom come in all forms. There are those built for momentum, those built for combat, and those built for fine-tuning your constructions.
And then there are those like the Hover Stone, used to keep things in place and act as incredibly useful stepping stones. The puzzles of Ihen-a Shrine revolve around Hover Stones very closely, and serve as a brilliant tutorial to the wondrous objects.
How To Complete Ihen-a Shrine: Midair Perch
The first room in Ihen-a Shrine gives you a glimpse into what Hover Stones can do. When activated, they hover - that is to say, they become totally immune to gravity. Other forces, when applied to them, will still affect them, but they will not fall.
In the first room, simply construct a small stepping stone ladder with the three floating Hover Stones and climb up to the second level before continuing on.
In the second room, use Ultrahand to Attach the metal grating that starts off leaning against the wall to the Hover Stone on the ground. Make sure you activate the Hover Stone by striking it, and then use the two objects as a makeshift bridge across the gap.
After crossing the gap, grab the makeshift bridge and bring it to the next gap. Rotate it so that it forms a slope up to the next level, and climb up it.
In the final room, first, use the two floating Hover Stones near the wall to create stepping stones up to the alcove with a chest in it. It's located right by the entrance to the room.
Step on one Hover Stone, use Ultrahand to move the other Hover Stone a little higher than you and then climb up it. Then, raise the first Hover Stone higher again, and you should be able to use that to reach the chest, which contains ten Arrows.
To actually get to the other side and reach the shrine's exit, first, place the nearby ball on top of the Hover Stone floating next to the contraption. Attach it so that it doesn't roll off when moved.
Hit the switch next to the contraption and watch as the Hover Stone glides across the gap.
Repeat the process, but with you standing on top of a Hover Stone this time. Fire an arrow at the switch to get pushed to the other side. Once you make it, put the ball from the first Hover Stone in the slot, unlocking the shrine's exit.