Hello. This is my first guide. I wanted to put something good on it, and this good thing is Olaf. He is my favorite character, and it works pretty well for me. In my build, he can tank. He can cause damage. HE CAN, AND WILL BURN YO ENEMIE'S HOUSE DOWN. I hope. It works for me =P In that build, looks like a normal damage dealer, with 260 ad, but the secret is in armor penetration. Destroy turrets LIKE A BAWS. Melt Rammus LIKE A BAWS. Destroy nexus LIKE A BOOOOOSSSSS. I hope. Well, try it =P I hope it works...

Oh, and sorry for bad english.

The items i chose were based on durability, so he can be on fights, and physical damage, obviously. Doran's Shield is a good choice, so hardly you will be First Blood's target, and his W makes him regenerate health with minions. Frozen Mallet is an item that helps him a lot in pursuits, and gives him a lot of health. Atma's Impaler is a item that matches with Olaf, giving him damage based on his health (a lot) and a bit of armor. Warmog, by the other side, is durability only. Gives him tons of health, and he can tower dive much easier. Bloodthirster is a sustain item, alongside with his W, making him regenerate health much quickly. Maw of Malmortius is basically, damage and durability.

I chose Ghost and Flash more as a utility spells. Enemie is running out of range? Flash and throw your axe! Done! Olaf do not have much mobility, needing to walk all the way to the battle, or out of it. Champions like Miss Fortune and Rammus will easily catch him. So Ghost out of there and run to the hills!

Pros:
Medium damage and good cc
High health and medium armor

Cons:
Can't go in and out of battles easily
Bad early tower diving

It is really easy to farm with Olaf. Use your Q the closest to the minions and to you, so you can easily grab your axe and deal damage. In late games, where farming won't be such a problem, but big minion waves will, get on the side of the wave and throw your axe in a way it will hit almost all minions. Againt super minions, i advise using your W and E to farm.