Although Princess Zelda has appeared in just about every Legend of Zelda game to date, with only a few exceptions, fans of the series have very rarely been able to play as the titular princess in a game that was canon to the overarching story. This would all change once Age of Calamity was announced and it was revealed that she would be a playable option in the prequel alternate timeline of the game.
Even though Zelda was playable in the original Hyrule Warriors, her gameplay in Age of Calamity is vastly different, mostly due to the fact that the previous playable Zelda was based on her rapier wielding incarnation from Twilight Princess rather than the inquisitive, younger version shown in Breath of the Wild.
Rune Playstyle
Zelda's first weapon is very simple in execution, though has incredible depth and is much harder to make the most of than the likes of Link or Impa. Aside from using the Sheika Slate in a very unique though simple way, the Slate also causes the main Rune abilities to deal increased damage when used and emphasizes much more use of them than any other character. For the most part, the Slate is designed to be used in combination with the Rune powers to increase their efficiency as the standard combo is fairly basic and short.
Sealing Power Playstyle
The second of Zelda's weapons is unlocked late in the story, though it is possible to obtain one of her Light Bows early through a Zelda or Sheika Amiibo. Zelda's Sealing Power is, like the Sheika Slate, a good mix of single target and horde combat, though its main power comes from its secondary form, where she deals increased damage at the cost of draining the special meter. Like the Slate, Zelda's Sealing Power is a little complex, though once you get the hang of it, she can be one of the strongest characters around.
Strong Attacks
When using the strong attack with the Sheika Slate, Zelda will create ice blocks on the ground which can not only be detonated to deal damage but also gate enemies in to keep them at arm's length, very similar to how Daruk's magma works. If used multiple times in quick succession, she will also summon an icy stairway which can be used to reach Wizzrobes in the air or start air combos.
The sealing power strong attack simply adds a ring of light to the target, which causes them to take more damage from light arrows fired by Zelda. This is similar to Ghirahim's tethering powers in Hyrule Warriors, though it can be applied to multiple targets.
Special Attacks
The Sheika Slate's special attack will cause Zelda to take a photo of everything in front of her, doing huge damage as she tears the image from the Slate. This attack has some limits on either side of her, however, as the Slate zooms the image in so show the world from Zelda's perspective, so some enemies have come out unscathed. The Sealing Power will shoot a light arrow in a narrow band in front of her almost identically to Zelda's Rapier Special Attack in the Hyrule Warriors, though the damage can be increased when combined with her strong attack's ability.
Basic Combo Strings
The Sheika Slate's basic combo is very short, tied with Revali's grounded combo for the shortest string, but it is capable of dealing with both hordes of enemies as well as single targets. The Sealing Power's basic combo is limited to dealing with enemies in front of her, but this changes when she is in her illuminated form as she is able to deal massive damage all around her depending on which kind of attack is being used.
Weak Point Drainers
The Sheika Slate's first combo, when upgraded a few times, is the best weak point drainer Zelda has access to, though the Cryonis Rune can also deal significant damage if used at the right time. For the most part, Zelda will have to combine her attacks with Runes to get the most out of them and drain weak point gauges more effectively.
The Sealing Power's third combo, where she shoots the target with light arrows, is the best weak point drainer when combined with her strong attack or second combo, which adds a ring of light to the target which causes them to take more damage from light arrows.
Defending
Both of Zelda's weapons don't allow her to move all that much when she fights, as she stays relatively stationary while performing her combos. Along with the fact that neither of her weapons have shields, it is best to just dodge with both weapons, though this can be offset by the fact that both of her weapons have quite a long-range, meaning you can also simply stay out of strong enemies ranges while still keeping up the pressure.
Weapon Modifiers
Both of Zelda's weapons greatly benefit from the Increase Attack Range modifiers, since her movement is very limited compared to other characters when attacking, as well as the Normal Attack increase modifier since both weapons have very fast standard strings that can be repeated in quick succession. Dash Attack Damage can also be useful on the Sheika Slate, as Zelda's dash attack changes from attacking straight in front of her to attacking all around her and is good for starting her first combo while dealing with hordes of enemies.
Unique Actions
The Sheika Slate's unique action will "activate" the runes, which just means detonating them in the same way as Daruk's magma, though each Rune has a slightly different effect and is best used in combination with multiple Runes at once. The Sealing Power will simply cause Zelda to float in the air and deal considerably more damage as well as change her combos, but her Special meter will be consistently draining, making her more along the lines of Young Link's Fierce Deity Mask from Hyrule Warriors than any of Zelda's other weapons.