First of all, the following guide is based on experience gained from playing Kayle. I apologize for not having all the cool icons and making it look flashy, but I promise that the information will help you become a strong Kayle player.

Don’t knock it ‘till you try it; good luck trying it. This build requires time to develop. Bot games are too short to get all of items, so you will have to try it out in a real game. Just right down the item build sequence and follow it as you go throughout the game.

Runes are a personal choice. They are better used to fill in the holes of your personal playing style. If you find yourself too weak to magic, physical attacks, or you are too slow, your runes will help you overcome the deficiencies.
My personal choices are flat Magic Penetration marks (greater mark of insight), Gold/sec seals (greater seal of avarice), and Magic Resist per level glyphs (greater glyph of shielding). My quints are two flat attack speeds (greater quintessence of alacrity) and one flat health (greater quintessence of fortitude).

In offence, I max out summoner’s wrath, brute force, sorcery, and arcane knowledge. Why? To get to the 10% mana penetration.
In defense, I take 1 of 3 in resistance, and full on hardiness and vigor. Why? The health regen makes it easier to stay more in the lane. The more you stay in the lane, the more experience you will get.
In utility, I max out good hands, swiftness, greed, wealth, and improved recall. Why? You need to buy expensive items as soon as possible.

Alternate between E (Righteous Fury) and W (Divine Blessing) as you level up. Get one level of your Q (Reckoning) at level 5 but max it last. Get your ult at 6 and then simply continue alternating between leveling up E and W throughout the game. Level up your ultimate whenever it comes along.

Throughout the game, only attack with your E. Your regular attack is too weak to be of much help unless you are last hitting. Even then, using your regular attack to last hit requires you to get close to enemy champions and incur damage. Since the primary spell you will be using is your E, the time between cool downs is enough to regenerate your mana, unless you have to use your W to heal yourself or a nearby champion frequently or you are leading an attack with Q.

At some time before starting play, inform your team that you will not be playing a support role. LOL is role oriented, so if you pick a tank, players expect you to display tank behavior. Kayle is known to be a support champion, which you will not be doing, at least not in the typical sense. You are a support in the sense that you will impart damage to enemies and use your W and ult to help teammates. This build develops a role that requires you to act more as a DPS carry. The key rule is:

Be as aggressive as your ability to survive will allow you to be.

Constantly be watching the life of your teammates. Whenever you can, heal other champions with your W. Ult the carry as long as they can win a battle and get as many assists as you possibly can.
Do not complain that somebody is stealing your kills. As long as the enemy champion is dead, you will be up on top.

Do it and do it often. The key is to ‘not die.’ When to ult yourself is a much better question. When you are 1v.1, be like Tyndamere and ult yourself when you are nearly dead. If you ult yourself too early in a battle, the enemy champion will simply run away, wasting your ult. Kayle is not fast enough to chase anybody down, so trick them into believing that your ult is down and ult yourself once they become committed to killing you.
If you are being chased, make a decision as to whether you can run away or not. Ulting yourself only to die a couple of seconds later is a waste of an ult. It takes a lot of restraint to not ult yourself when you are running away, but smart players known when to ult themselves.

1. Thou shalt never overextend yourself. It will only result in death.

2. Thou shalt never tower dive. It is a waste of an ult and you will more than likely die anyway.

3. Thou shalt ult champions who are on the verge of death, but only if together you can win the battle or they need a little extra time to escape a bad situation. Ulting a champion who is surrounded by 5 enemies is typically a bad idea, unless your teammate is op and just needs a little extra time to get the penta kill.

4. Thou shalt not apologize when you didn’t ult a champion and they died. Inform your team that it is their responsibility for not dying, not yours.

5. Thou shalt farm: minions give you gold, gold gives you better stuff, and the right combination of stuff makes you awesome.

6. Thou shalt be in every team fight, not in the middle, but on the edge. Be ready to ult whoever is being targeted but only if the above rules are met.

7. Thou shalt use Q as a slowing spell. In a regular fight, lead with your Q but then rip damage with your E. Sometimes you can use Q as a last-hit spell. Don’t use it to farm; it is a waste of mana. Getting items to max the power output of your Q is lame.

8. Thou shalt never chase a champion by yourself. You typically can’t chase them down for various reasons. Your Q has a short range. E attacks are basically auto-attacks and require you to come to a complete stop before attacking during which they are running even farther away. Plus, late game, chasing is bad. You will nearly always get ganked and then you will die. Always be with your team. W the champion closest to the enemy.

9. Thou shalt auto-attack. Put yourself in a position where enemy champions have to come across your effective range as they run away. No mad button clicking, just point to the guy you want to kill and click once. For some crazy reason, your first strike takes longer than subsequent auto attacks. Button mashing is just going to move your character between strikes and you will not attack as quickly. Twitch players are excellent at this skill.

10. Thou shalt never, ever, EVER, give up. It takes time to put together all of the items for Kayle. Until you get ALL of the items together, you will not own anything other than your LOL T-shirt. There will be games when your team is down by 15 kills that are still winnable as long as you get all of your items. Surrendering is for losers. You are not a loser. You are the hidden weapon.

For some reason that I cannot explain, the order in which you buy the items is very important. Perhaps it is because the items are linked to the type of game play required (early, mid, late) at different points in the game. All of the numbers here are the gold required to purchase the items. Regrowth Pendant is 435 g or rather, it takes 435 gold pieces to purchase said item. Knowing how much item costs helps a lot in knowing when to teleport back to base.

1. Start by getting a Regrowth Pendant (435 g). That’s it. When you have 725 gold, get some Boots (350 g) and a Philosophers Stone (365 g). It is very important that you get back to fighting as soon as possible. I normally W myself and use Ghost. Teleport is another option.

2. Get your Boots of Swiftness (650 g).

3. Save up for a Recurve Bow (1050 g).

4. Buy the Ionic Spark (1180 g). Use your new toy, coupled with your E, to really start farming minions.

5. Buy an Executioners Calling (1350 g). You can buy it in pieces (Brawler’s gloves (400) and Vampiric Scepter 450) or outright, depending on your gold. If you buy it in pieces it will cost 500 gold.

6. Buy a Kage’s Lucky Pick (765 g). It is cheap; get it as soon as possible after getting your Executioners Calling.

7. Buy a Phantom Dancer (2845 g). Normally you will do this in two steps, first a Zeal (1195g) and then the Phantom Dancer (1650).

8. Wait until you have nearly 2000 gold and sell the Ionic Spark (1610 g). Buy a Thornmail. By now, you are becoming mega squishy. Thornmail will cure your squishiness.

9. When you have 3600 gold, sell Kage’s Lucky Pick (283 g) and buy an Infiniti Edge (3830 g).

10. When you have 3400 gold, sell your Philosopher’s Stone (400 g) and buy Madred’s Razors (3800 g). When your team is ready, yell out “ZERG RUSH!”, and begin the pownage.

Every hero has a kryptonite. Kayle’s is being blinded or silenced. For example, enemies pop out of nowhere. You could kill them but you have to activate your E, which of course, you can’t. You then become the recipient of some crazy burst damage. You can survive if you can ult yourself, but you can’t. Sad day. Some champions are very good at silencing. The only advice that is helpful is that AS SOON AS YOU SEE THEM, ult yourself and attack. Utling yourself and running away seldom works since you are typically also slowed. When your ult wears off you are going to get creamed.
In reality, the above only happens when you have overextended yourself. Do not overextend yourself; you will always die.