Kayle is probably one of the most under-rated champs. She is known to be squishy and have low dmg output. This is a horrible misconception, if played correctly, Kayle can have a positive kd every game. If Kayle gets fed, she is unstoppable and can kill soo many characters that are considered "normal" or "OP". If you have the build show above or the same build with a Bloodrazor instead of the phantom dancer, you should be unstoppable.

First you buy a Doran's ring then rush a Nasher's Tooth or Ionion Boots. By level 4 or 5 you should get blue buff. You're CD should be rediculously low so you should be able to freely spam your abilities w/ blue buff. From here you should get a hexgunblade, followed by a trinity force. Depending on how tanky their characters are you might want to buy a Madred's Bloodrazor. If they aren't get another hexblade or Zhona's Hourglass (that way you can become invincible after u make someone else invincible). Your final item (after you sell your Doran's Ring) could be a hexblade, a rageblade, a nashor's tooth, a trinity force, a crystal cepter, rod of ages (if you get this you should rush it earlier), or a ghostblade.

The build I show above is generally my preferred finished build (the game is almost always over by the time i would have to switch out boots for a phantom dancer), but i occasionally have a rageblade if my team doesnt have very good dmg output. But MORE OFTEN i will have a bloodrazor instead of one of the hexblades in case they have very high hp champs, and the att speed is nice too.

Pros
great damage output
good support
lifesteal is amazing on her
Cons
squishy when stunned
slow movement at the start of the game
slow attack speed

Use Clarity and Flash.
Clarity is a MUST because she uses manna like no other.
Flash is just good for getting out of tight situations.

Other abilities could include ghost (with ghost switch the flash point for the ghost point), exhaust (with exhaust you should switch your deadliness for cripple and get rid of the point you spent on Flash), and ignite (with ignite you should switch your Presence of the Masters mastery for Burning Embers so you get the extra 10 AP and use the point you used on Flash for something else).

Between all of the optional spells i generally would use exhaust instead of flash than any other.

Other builds generally have you get reckoning first, but i find righteous fury as a better starting spell. It makes you a ranged character and helps with farming alot. i then get divine blessing for survivability in the lane. This coupled with your doran's ring and clarity will allow you to last a long time without having to blue pill. I usually just keep upgrading these two skills until my divine blessing is lvl 2 and my righteous fury is lvl 4 at which point i get reckoning lvl 1 just for the slow effect. if you are laning well then i would get it earlier as shown above in the skill sequence chart.

Now any experienced kayle player would say "reckoning is the bread and butter of kayle's dmg output." This is partially true, however, i like to get the reduced CD on Righteous Fury in order to have a high level of harass. Besides this, i find that reckoning has a very high manna cost and low dmg output alone. Thus i wait to upgrade this ability in late game in so that kayle has the manna to support the ability.

However, in a normal game i will get reckoning as my lvl 3 summoner skill and keep upgrading divine blessing and reckoning.

Most of the Runes are for CD so that you can spam her abilities. I also include movement runes so that she has at least above 400 movement speed by the end. This will allow her to be quick enough for pursuit with divine blessing. I also include magic pen runes for extra dmg. Since this build slightly leans toward AP and all of her abilities use AP, i choose magic pen runes over att pen runes.

Other runes for consideration are att pen runes, hp runes, movement runes, ap runes, ad runes (i wouldnt suggest this unless u have ap runes to boot), or att speed runes.

The slow from reckoning and your hexblade will make it difficult for enemies to flee from you or catch you if you are running. i usually always use intervention to tower dive or if you have a pre-made team to tell one of your allies to dive (like a master yi since he is much faster than you). With the reduced CD your intervention spell should not be wasted but still isnt necessarily needed to be used sparingly. biggest thing with this build is to spam your abilities and get blue buff if you can.

Use intervention on those who are about to die. It can also be used as a sort of Banshee's Veil for Karthus's ult. Use divine blessing often. As I said above spam all of your abilities in a fight. If you have blue buff you will be able to spam constantly.

Farming is a bit more difficult with Kayle until you get to the higher levels. just try to time your righteous fury to last hit as many minions as you can.

If you generally follow this guide it should help with you're playing as Kayle. My personal preference is to rush a Rod of Ages or Nashor's Tooth. This build is expensive but effective i find.