This is my first guide, and it is dedicated to Olaf.
Olaf is the ultimate "Tank Slayer" on the battlefield aswell as a good jungler/lane ganker.
This build focuses HP and some defense. Olaf is overpowerly strong when he gains HP becuase of Vicious Strikes damage increase.
Also he gets a nice amount of Life Steal with Vicious Strike active, and the attack speed from Olaf's passive. Only the 2 of them will keep Olaf alive for quite some time to deal a great damage output in a matter of seconds.

Pros:

Unstoppable 1v1
Great survivability
Nice slows
Insane damage output
You can focus HP and defense, still the damage is good


Cons:

Not so good against ranged if you find Undertow aiming hard.
Undertow is hard to master.
Requires slight braincapasity.
Not cool looking unless you buy a decent skin.

The reason for my choice of items:

I would rather have Dorian's Blade instead of Dorian's Shield because of the damage and life steal, I need this damage for my Undertow harassement.

I buy Berserker's Greaves for attack speed rather than Mercury's Treads for tenacity because Olaf's Ultimate removes any stun/slow/fear and he cannot be disabled during that time either.

Next I go for Phage to build up Frozen Mallet. Frozen Mallet is a MUST for Olaf, the HP and slow you get from this item is incredibly effective as you will see people will run for their lives when they find out how much he actually hurts to face in close combat. You will have them slowed at all times with Undertow for ranged and keep them slowed with Frozen Mallet.

Now you will have sufficient HP to go for Atma's Impaler already, and this will really buff your damage aswell as it gives nice armor and a bit of crit.

Then it's time for Warmog's because of the crazy HP gain, so remember to farm when you are nearby minions to stack this fully up as fast as yuo can.

Now you should be able to have some easy and fast kills out there to get B.F. Sword and Bloodthirster for more damage and life steal!

If the game keeps on going for a long duration or you get superfeeded go for Phantom Dancer to improve speed. More speed = more damage, better life steal and easier chases for close combat.

Berserker Rage Passive
will help you strongly, especially in 1v1 combat.
Undertow
Perfect for harassement early game, also nice damage for a ranged attack. This damage will not increase much, so max this later for the slow.
Reckless Swing
Super damage output, so max this quickly.
Vicious strikes
For improved damage and life steal!
Ragnarok
Will help you in both crushing enemies and escaping, it's the best ever!!

My personal choice is Exhaust and Ghost.

Exhaust for easing up a 1v1 if I can see that this won't work, suddenly I have the controll again. Or for escaping.

I use ghost for either chasing, fast turret diving or escaping with Ragnarok active.

Precombat

Use Undertow to harass and lower their HP. If you are skilled you will have a great Undertow hit when you engage so they won't be able to get away from you when you strike.

During fight

Start with W-E-Q
Keep on Reckless swinging as often as you can.
When you are close by the champion you want to eat grass, don't throw your axe too far, try to be quick and toss it close by, when he picks it up, it almost resets the whole cooldown which means you can toss it again early = more damage.

If this looks like a tough fight think through if it's worth using Ragnarok for Armor and Magic Resist in case of a gang with stuns/roots/slows etc. Rather Exhaust or Ghost away then.

Olaf is also great early game to "turret dive". This is how I mostly get my First Bloods. Pop Ragnarok, Ghost and Exhaust, do your thing and run out of there!!

Well, that was all for now. I will be back editing / adding new info if I have new or other suggestions.

Thanks again for stopping by to have a quick look and I hope this will help some of you :-)

- Calypzy