This is AP Garen.
It's not played the same way as tank or AD, so try not to hold it up in comparison. I built the items with synergy in mind so I'll explain each item in order.
The main goal of my AP Garen is to be able to focus down an enemy tank in about 2~3seconds or less while the rest of the team targets someone else. He's built to emphasize his burst damage and intended to jump into a fight, grab a kill/turret and jump out again in time to push a different lane (with teleport).
First sheen for more damage on his strike, and boots to move faster.
Then upgrade sheen to lich bane.
Then go straight full a full deathfire grasp. This item works very well with Garen's ultimate. Trigger the deathfire on a tank, strike with lichbane's bonus and then ulti and the tank should go down every time.
Next grab a Malady if the tank is building for magic resist to counter Garen. Otherwise you can probably skip this item.
Grab a Hextech Gunblade for the active 50% slow effect. At this point anyone you attack should die but in a team fight you want to be able to catch people trying to escape and this works well.
Last is the rabadon deathcap. I get it for the big boost it gives to your deathfire and strike. If you don't get a malady, feel free to get 2 of these.
If hextech gunblade feels unnecessary (for example, you're playing against a lot of melee characters) you could always swap it out for a frozen mallet instead. It can provide a little extra survivability and still gives you a slow effect although you do lose a little damage for going that route.
Garen is considered to be pretty tanky, but in this build your items don't really improve on that. So to offset your items, build garen for armour and magic resist late game. His shield works well enough to offset the items early game.
So here's what runes you should get :
Armour penetration marks. (x9)
Gradual armour seals. (x9)
Gradual magic resist glyphs. (x9)
Gradual armour quints. (x3)
Flash and teleport. Garen's Ulti cools down after 1.5~2 minutes. With these you should be able to gank a lane and push a tower every 3 or so minutes after you get deathfire grasp.
In my opinion, the best way to use these are to hide in a bush and attack from behind. Then, flash in front of them as you enter a tower's range to avoid taking the extra damage. The teleport can be used to get to a lane or get back to your own, use it as necessary.
I get Garen's Shield first because it's passive gives a good stack, but I stop after rank 3 because the runes you have begin to compensate at this point for the other 10 stacks. That's why I max Decisive strike after getting the ulti (also, you should have lich bane by level 9 so that can make full use of the item). I finish off the shield after this.
I don't get the spin attack until the very end because I don't really use it that much as an AP Garen. Flash is enough to get away usually and using this skill right after flash can remove a slow effect if you happen to be affected by one.