Kayle is one of the Best Hybrids in the Game that almost no one Knows about
I Prefer Kayle Over Jax Simply Because she is a ranged Champion and because Jax can be easily Countered with Sword of the Divine.
She is one of the Best DPS Champions in the game that No One knows about.
One of the Cheapest Champions to purchase and to grasp the Concept.
This guide is to show you how good she really is, and the fact that she doesn't have to be a Support or an off Tank

"All Champions are op if you know how To play them Right"
You Really Can't Harrass the life out of people early game.
Once you reach level five you can be able to Outfight and Destroy your lane, mostly targetting the Squishy Ap/Ad carries in your Lane (Altough you can Kill Tanks early game too, i Prefer to shut down the Squishy Carries).
Keep in mind that you may also be laning with another Ad or Ap carry, and they will want the last hits for themselves (This has happened to me many Times,).
So take all opportunities when Your Lane partners goes to Base to Heal, Or just Use Her range or reckoning to get in some last hits.
You can Also Jungle with Kayle after she gets a Rageblade (If your Team already has no Jungler)
She is a great Deceiver much Like Olaf, And Kite enemies into a team Fight, Use your Op Ultimate to your Advantage and Destroy them with Reckoning and Righteous Fury.
Kayle is increadibly Item dependent and you cannot kick peoples teeth in untill you atleast have the rageblade and Stinger Available (Or have a Decent Laning Partner)

Pros:
-You are increadibly Nasty Mid to late game
-She is a great Carry
-Increadible high damage out put due to the attack speed
-You can tank enemies with your immunity and lifesteal/spellvamp
-Great Farmer mid-Late game
-Can Shield/Heal Allies
-Shes Great for Anti ganks (Slow the Ganker and Speed yourself or your Ally)
-Great Ganker
-Prevents People from Running Away
-Great at Diving Turrets
Cons:
-Increadibly Item Dependent
-Really slow start
-Mana Dependent early game
-Very Squishy
-Slow farmer untill you get rageblade and a stinger
-Can easily be Targeted in Team Fights

Core Items
Guinsoo's Rageblade: This will be your Main damage/harassing item you will need very early game, and it makes her Reckoning into Righteous Fury combo Much more Effective
Berserker Grieves: I personally get these just for the Increased attack speed to help you in the Laning Phase.
Nashors Tooth: This Item will Allow you to Permanently Have Righteous Fury on, the Duration of the Spell will End after the Ability is off cooldown, you can now Spam Righteous Fury. It also gives you more attack Speed and mana regen.
Malady: Malady works great because of the extra attack speed and it also goes well with her new Passive and further reduces the Armor and Magic resist.
Hextech Gunblade: This item will slow your enemy down, (after you hit them with Reckoning) and make an enemies Escape inevitable. It also gives you Ad, Ap Lifesteal and Spellvamp, Allowing you to Tank/Duel with the Others teams carries.
The Last item, You can Chose Between a Phantom Dancer, The Black Cleaver, Or a Bloodthirster. Though most of the Time, the Game is over by the Time you finish the Gunblade. and it Depends on what you want, Movement or Attack speed, More Lifesteal, or to Shred their Armor some more

I max Reckoning First, simply because of the amazing damage it does to the Enemies Squishies, and its Sshort Cooldown
I Max our Righteous Fury after Reckoning for the incraed Splash damage.
I Max Divine simply because the Heal and Speed Bonus are not increadibly significant untill Late game
Intervention is Probably one of the best Non-Offensive Ultimates in the game. Altough you mush Always use it Correctly. NEVER cast it on Your tank, Altough its Nice to save them for an extra three seconds their damage output will not be able to turn the tide in a teamfight.
Try to save your Ult for yourself to reduce the burst damage you or On of your Ap/Ad carries will receive.
DO NOT to waste it on a Fleeing Ally, Chances are they won't noticed Theyre Immune to Damage and will continue running away.

After getting in Many more Games as Kayle under my belt, I've tweeked this build a bit. Every game will have different enemies and you will have to Adjust to the Changes. I Always rush Guinsoo's Rageblade simply because it is essentiall early on. After this i NOW Farm for a recursive Bow, Which you will either Build it into a Sword of the Divine (For the Enemy Jax) Or start on Madreds Bloodrazor for the Tanky champions. You will interchange these, and sometimes have to get both items for your match. By now you should be crushing creep waves and going for Your Hextech Gunblade and Bloodthirster. I Build Nashorrs tooth last simply because it Never gives me enough damage early game.

I have had games where the Laning phase is over by 15 minutes and the game is already decided, Your job as the Ultimate Wildcard is to see if you can build fast enough, and Kill your enemies. It sounds weird, but i actually prefer to Solo mid as Kayle, Simply because of her Reckoning into Righteous Fury combo simply devastates Squishies. Plus She has Natural sustainability with her own minor heal and can always make it out with low health. Always try to be the one harrassing in your lane. And NEVER use Intervention Prematurely, it might help You Save an Ally from Requim or Vladimir's Hemoplague.

This is essential to All successful Kayle builds, since Kayle is extremely item dependent, a Match can be Determined if you could build Your Items fast Enough. Try to use Righeous Fury as much as possible to famr up the Creeps, If your Opponents constantly in your face then simply last hit with Reckoning. Her farm is only a problem early game, where she simply doesn't have the damage output, but once your have items, you will be Amazed at how she can Destroy entire creep waves with 6 Autoattacks.

I Take Exhaust to cripple the enemies Ad melee carry or ranged carry, and helps you catch up to a feeling enemy, and ignite helps finish off that pesky Tryndamere or Swain