This is an easy build to execute, because it uses only the recommended items, which are easy to find in the store. What I think matters most is the order in which you buy the items.

Kayle is one of the few champions that costs 450 influence points, so many beginners may use her and this build is great for beginners.

The main points of focus in this build will be attack speed, attack damage and ability power. I believe Kayle benefits most from those three main skills.

I selected 9 Greater Marks of Insight to increase her magic penetration, because Kayle usually deals more magic damage than physical damage. With magic penetration, Reckoning and Righteous Fury will deal more damage. Since I like to keep Righteous Fury activated indefinitely, magic penetration will benefit every attack.
I selected 9 Greater Seals of Clarity to increase her mana regeneration, because if you're casting her spells as often as possible you will be running low on mana. I like to keep Righteous Fury activated indefinitely to turn Kayle into a ranged attacker, which uses 45 mana every ten seconds after her cooldown reduction rate is 40%. Mana may run low if Kayle casts Reckoning as often as possible to keep enemy champions at bay. If an enemy champion gets close to Kayle you'll want enough mana available to cast all her spells.
I selected 9 Greater Glyphs of Force to increase her ability power, because both ability power and attack damage are important for this build. More ability power makes Reckoning very powerful, since it gains damage equal to Kayle's ability power. More ability power also adds more magic damage to every attack while Righteous Fury is active, and since Kayle will be able to keep Righteous Fury activated indefinitely with this build, she will deal additional damage with every attack.
I selected 3 Greater Quintessences of Alacrity to increase attack speed which helps Kayle deal more damage and farm more gold. Attack speed is great when Guinsoo's Rageblade has already been purchased, because you will stack the extra attack speed and ability power even faster.

These Rune selections support the items Kayle will use, which give similar bonuses.

I've focused the masteries on the Offense Tree which gives Kayle a little extra boost while attacking. Cripple is important get the most out of Exhaust, because Kayle will deal more damage to exhausted enemies. Ability power, attack speed and attack damage are all increased.

I've put the remaining points into the Utility Tree to get Insight, which makes Clarity more helpful to your team.

These masteries assist both the Summoner Spells I've chosen, give Kayle a small experience boost and help with farming due to the small attack damage boosts.

The first main item I want to buy is Nashor's Tooth, it is a great item for its price and the items required to build it are quite helpful in the early game. Attack speed and cooldown reduction rate are important to Kayle early on. So you'll buy all Nashor's Tooth requirements first. The first required item you'll buy is the Dagger, which grants Kayle a 15% attack speed increase. Next, you'll buy another Dagger, to further increase the attack speed bonus. Then you'll get the Stinger, which increases your attack speed bonus to 40% and adds 10% cooldown reduction. Next is the Maki Pendant, which grants a small mana regeneration bonus that is very helpful early on. Then you'll get the Amplifying Tome, which adds 20 ability power. Now you'll be able to get the Fiendish Codex, which reduces your cooldowns by 10% more. Finally, you can buy Nashor's Tooth.

The Ionian Boots of Lucidity are next, because they will complete the max cooldown reduction rate of 40% and add a movement speed bonus. You'll have to buy the Boots of Speed first. Now Kayle can cast Righteous Fury as soon as it expires, so she can have it activated indefinitely, dealing damage and splash damage from a distance.

Doran's Ring is next because it is easily affordable and gives you a small mana Regeneration boost, which you may need because you're casting spells continuously.

Next you can get Guinsoo's Rageblade, Hextech Gunblade and the Trinity Force. I prefer to get the Trinity Force first of these three items if possible, although it's more expensive, it gives Kayle better advantages.

I get Righteous Fury first because it helps with farming gold, which allows you to buy items earlier in the game. Also, it works great with the increased attack speed you will acquire with your first item purchase, the Dagger, and it keeps you out of danger early while you are still weak.

Get Reckoning second so you can effectively attack enemy champions. Divine Blessing is good for the speed bonus if your chasing or escaping, but its healing effect is not great, so it is the least important spell. Get Intervention when possible, so you can help your allied champions escape or survive a little longer.

I selected Exhaust and Clarity.

Exhaust allows you to catch fleeing enemy champions. The Cripple mastery makes this spell much better. Casting Reckoning to slow the enemy champion and deal damage, followed by Exhaust, then Divine Blessing on Kayle to grant a speed bonus and Righteous Fury to allow Kayle to attack from a distance, the fleeing enemy champion will be in trouble.

Clarity is very helpful when you're engaged in large or long battles and run low on mana, it also helps your allies. Since this build includes the Insight mastery, your allies will benefit as much as Kayle does.

Righteous Fury along with the increased attack speed is very helpful for killing minions and getting last hits. Kayle will also have the maximum cooldown reduction rate, allowing Righteous Fury to be active indefinitely. Both attack damage and ability power help deal extra damage with both Kayle's main spells. Kayle will be able to push a lane solo versus enemy minions and an enemy champion during the late game, while she can still hold a lane during the early game and farm gold.

This build will make Kayle very effective late game. Her attack speed will be almost doubled, and gets faster with each hit, up to 8 times, thanks to the Guinsoo's Rageblade. Reckoning is quite powerful with the added attack damage and ability power, and it can be used often. Righteous Fury can be active indefinetly, making Kayle a ranged attacker, which keeps her safe. Kayle can also retreat quickly with the use of Divine Blessing.

To engage an enemy champion, Kayle can cast Reckoning to deal damage, slow the enemy and allow Kayle to deal more damage with attacks that follow. Then she can cast Righteous Fury, if it is not already active, to deal damage from a safe distance. If the enemy begins to flee, cast your Exhaust to slow them and cast Divine Blessing on Kayle to give her a movement speed boost, allowing you to catch up and continue dealing damage.

If you try this build, please comment here or message me with some feed back.

Thanks!