Reckoning is powerful even at lower levels and Kayle can utilize this advantageous ability to dominate her opponents in early game; caution should be taken in its use, however, as it is a mana-costly spell to use repeatedly.
Divine Blessing can be used for sustaining in lane or for harrying allies to a position or lane all the while healing them.
Righteous Fury's allows Kayle to deal damage even when blinded or being dodged, as the magic damage on-hit is dealt regardless of if the attack damage on-hit is being negated.
Righteous Fury's will damage turrets only if the splash damage is applied indirectly, such as when creep waves directly under a turret are attacked.
Righteous Fury causes full damage to all other structures if they are attacked directly.
If Righteous Fury's duration ends while Kayle is in the middle of her attack animation, she will hit the target, but neither the bonus damage nor the splash will be dealt. The attack is considered ranged.
It is possible to hit enemies easily while staying at the back of your minion wave by using Righteous Fury. This can be accomplished because not only does the splash damage 'spill' over to nearby enemies when you last hit a minion, but also allows you to harass melee enemies. Staying behind your wave in this fashion will let you wait for cooldowns and heal yourself or allies.
Putting a point into Righteous Fury instead of Reckoning at level one may improve your ability to harass and stay in lane due to its lower mana cost and more continuous effect/duration.
Intervention is also an effective ability to bait enemies to attack or turret dive at low health making them commit to killing your ally or die.
It may not always be best to Intervention an ally when they are nearly dead. If they are about to receive a large amount of burst damage (such as Champion combo), shielding them will absorb more damage than if you were to shield them just before death (which may end up saving their life or prolonging it more effectively than if you had waited until the last second).
A Essence Reaver is also a good item for a build oriented in attack damage. Combining with attack speed itens/runes/masteries, you will never run out of mana. However, rushing it is not recommended, because it not gives any attack speed.
Consider building Iceborn Gauntlet if supporting, as it gives mana, cooldown reduction, armor, a bit of ability power, and a Spellblade passive that creates a slowing field.
If she starts to weaken she will likely use Intervention to quickly turn to tides of the duel and kill you. Because of this avoid duels that last too long.
Kayle has very fast and strong snowball skill, make sure to deny her kills as it will hasten her late-game supremacy.
Watch her build carefully to know what to do:
If she is AP (most likely with large amounts of AS) she must be immediately shut down as she will scale into a deadly powerhouse late-game, but is very weak early. All her damage comes from Reckoning and Righteous Fury. This build depends heavily on Intervention for survivability as Kayle is fragile, baiting her to using it on a wounded ally and switching your focus onto her will take her out quickly.
If she is AD she stands strong at all stages of the game, she does not depends much on her skills for damage and is somewhat tanky, she deals less damage than an average top laner due to lack of AD scaling on any skill apart from Reckoning and any AS or AD steroid. Later on Kayle will become akin to a second AD Carry albeit with the ability to become invulnerable, make sure to engage her in planned out fights, but don't fear her damage output much.
If she is supporting it's very likely that she leaves the role after a while, most likely deviating into the first mentioned build, but still taking care of wards and heals. Facing her in the bot lane can be very hard if you are unable to keep your distance, so be sure to pick a mobile or long ranged champion
Kayle is especially hard to beat in the top lane, due to overly outranging almost all other champions here. The few ranged ones, like Jayce, and the ones with long-ranged gap closers, such as Jax or Renekton, will have a much easier time against her.
Avoid dueling her late game as she will most likely have almost finished items. She excels at 1v1's due to her Reckoning and Intervention. This not only allows her deal incredible amounts of damage against you, but also completely negate any damage you can deal to her.
With 2092 health at level 18 Kayle has a very high natural health, abilities and items that deal % of max health as damage are effective against Kayle.
Try to force Kayle to use her spells and then back off, due to her high mana costs in the early game.
Kayle is vulnerable early game, burst damage can easily kill her.
Kayle can use Intervention to avoid damage, but while in this state she is still vulnerable to CC effects. Use this tactically when she turret dives to have her still take damage when Intervention's short duration wears off. (2 / 2.5 / 3 seconds).
On the other hand, Kayle abilities are short-ranged, and her pushing power is limited to Righteous Fury. As such, long range mages should to easily zone Kayle out. Keep in note that Kayle has natural sustain using Divine Blessing and can still use the ability to try and gap close someone using the ability's movement speed bonus.
A Randuin's Omen, Frozen Heart, or any other ability/spell that reduces attack speed is a good way to cut off some of Kayle's damage, specially if she bought a Runaan's Hurricane. (Just remembering that, the more attack speed she has, more effective will be the attack speed reduction.)