This is my first guide, I've been playing Kayle lately and destroying people in the Mid lane.
Here is my version of AP Kayle, I hope you find some useful information in this guide..:) Keep in mind this is a work in progress and will be upgraded as I get more information..

Pros

- very versatile

- nice slows/speed boost

- melee champion that can be devastating at a range

- self heal

- counters every champion with ultimate

- scales well with attack speed

Cons

- Running out of mana renders you useless

- Very standard play style/easy for enemies to read

- Tends to fall off end game

- A miss used ultimate can cost a team fight/ the game

- people get mad if you don't ultimate them when they dive turrets

Kayle has exceptional farming capability using her Righteous Fury. Generally what you want to do is try to auto attack the melee creeps without using Righteous fury then activate it and try to poke your enemy, if he runs farm the ranged creep... if he is out of position after the first hit try and chase him down using Kayle's Reckoning as long as you are not at risk of being ganked.
In my opinion keeping the lane pushed up to your opponents tower is great for denying farm and is hard for Kayle not to do anyways. If you're constantly pushed up to the opponents tower try to bully them out of lane when you have a siege creep so you can get some extra hits on their tower using Righteous Fury. If you get caught hitting the tower you can easily escape using Kayle's Divine blessing, even tho this will only be level 1 in the early phase of the game it is more than enough to outrun most champions and escape to the safety of your tower.
If you have the lane pushed to the tower and are worried about getting ganked you can instead take the wraith camp or wolf pack, if your jungler is busy of course :p
Always check with the jungler on your team to see if you can get the second and third blue buff. Blue buff will allow you to spam your heal ability making you extremely mobile and allow you to stay in lane longer than the enemies mid, Free tower? Sure why not!

After you have taken down your first tower and maybe helped secure a dragon kill, you should be looking for opportunities to get a kill on either bot or top lane. I prefer to gank lanes that have a pink ward on the river, since you lack any hard crowd control such as a stun or knock up.
Try to communicate with your team if your ultimate is available because this will allow any member of your team to sucesfully tower dive and earn you a kill or assist.
If you cannot secure your team a kill when ganking at least try to take down a tower. Keep in mind that the splash damage from Righteous Fury does not splash when attacking towers, however it will splash from a creep/champion and hit towers!