Firstly i want to apologize for my bad knowledge of English and say hello to you. So: Hi.
This is my first build which i invented with many hours of games played with Kayle, which is my fav champ.
I wanted to stress that my build is a variaton of many others, so be forgiving :)
Let;s start!

They are standard, for a bit. I think the AD runes will help you to stick into the ground your enemy, however the Res and Armor runes will protect you a bit, because of squishy Kayle

Pretty Standard

I was wondering what about masteries but i got to the point.
AD 9-0-21
This is the attacker way, you will get nice attack speed and armor penetration- the most valuable thing in way.
AP 9-0-21
If you add 3 points into the [ Mental Force then full in [*] Sorcery[*] and at the last one point in [*] Arcane Knowledge[*] you will get CD which is bit important. You will be able to spam your [*] Righteous Fury [*]. Especially when you have blue - then you got 0 secund cooldown.

The main thing and the reason why i am writing this ****ty article is the [*] Tiamat[*].This understimated will give you MP and HP regeneration starting items which makes [*] Tiamat[*] nice item to rush on. The AD Boost help you with harass and overall attack. But the main thing is his passive. With [*] Tiamat[*] and [skill] Righteous Fury[/skill] you will get enourmous AoE damage. You can imagine it like a chain reaction. Important feature is that you will make AoE Physical and Magic damage in the same time
Of course you need boots - [*]Berserker's greaves[*] are the best.
Then you should boost your AD or your survivability it's up to you, just look at the items sequence and make your choice.
Finally let's face it: your main tactic is to rush [*] Tiamat[*] but in the meantime buy your boots, then summarize your situations and if you are getting little smacked just buy [*]Phage[*] otherwise [*]Infinity Edge[*]

[/list]

You got two choices:
You can max first [*]Righteous Fury[*] which gives you better harass but i think maxing [*] Reckoning[*] gives you nice buff to your attack in the early game.
Obviously add your skill points in ulti whenever its possible.

Your main ***igment is to Farm ( you don't say?!) using your E.
Harrasing goes like this: just pop your Q then autoattack with E, it's simple.

Kayle is master of tower diving thanks to her Ulti, which makes her invulnerable to any attacks. Just use it when you are gettin <50% HP and FINISH HIM.

Nothing to said :)