With your sword out, damage yourself down to 0 hearts using some kind of knockback damage such as bombs. A split second before Link dies, there is a small time window to perform an action such as a jumpslash, sidehop, or backflip. Upon taking the damage and getting knocked back, hold L and mash A and B repeatedly. If successful, as Link is getting up from the knockback he will begin to rise off the ground. After you get off the ground, you can switch to only mashing B to gain height.
With each press of B while airborne, Link will perform a jumpslash, rising slightly higher into the air and moving slightly forward each time. Due to Link having 0 hearts, his jumpslash is immediately cancelled, and he returns to his normal falling stance, allowing you to jumpslash again. Providing the B button is mashed fast enough, Link may gain infinite height, assuming nothing knocks you down in the air. If you do get knocked down and land on the ground, you can start your hover back up from where you land, using the same process described above.
Unfortunately, due to Link having 0 hearts, as soon as you touch land or water, Link will die. There are three main ways to prevent this and successfully end your hover:
† - Upon loading the next area, Link will instantly die, however this can be used when hovering into areas where a death will warp you to the same map (such hovering into a dungeon)
There is a fourth, more complicated way to land a hover, as explained on the Storage page.
While it's possible to start a Zombie Hover off any means of damage besides death-warps, damage that knocks you down has the largest window to start the hover, and is highly recommended. This means that it is possible to start a hover with an enemy's weapon such as a boko-stick if you deplete your health using a large fall followed by a sidehop (jumpslashing from the ground isn't doable with an enemy's item, and nor are backflips). In Forsaken Fortress 1 this can be used to hover up to the hero's sword early, though this trick is very difficult.
Also, do note that if you have a bottled fairy, you cannot start a hover, as the fairy will revive you the moment you lose your last heart.
This allows you to get to heights not normally accessible, allowing new shortcuts and various item skips. Inter-island travel, allowing access to areas early.