INTRODUCTION
Olaf is a offtank he can kill very easy with Reckless Swing he can slow with Undertow and he can heal with Vicious Strikes now Olaf is a very hard champion to beat how much you make his health go down that much the attack speed will rise because of his passive.So Olaf early game can die but late game he is very powerful.Now his last spell Ragnarok is one of my favorite spells because he can't be disabled so it's a very good thing if you go first in team fights with your ulti.
SUMMONER SPELLS
So the summoner spells are very good because it's a very nice combo with the Ghost and Ulti you can use it even for attack and for escape you just run and nothing can stop you.Now the exhaust spell well first blood is very easy with exhaust they can't move and you just kill them and in late game because Undertow won't slow enemies a lot you will have to use exhaust.
RANKED PLAY
So Olaf in ranked played Jungle or Solo top but i really don't like Olaf in jungle because he is always on low Health in jungle so the other Junglers like Lee Sin Warwick and something else can kill you very easy.So that's why you will play Olaf solo top he is very good at it i play Olaf solo top even in normal games 1vs2 and at the end you will be the strongest int the team.But remember this if you play him solo top play him defense and if you play him in a lane with another champion than play more offense.
TEAM WORK
So team work you will always go in team fights with your ulti because every one will throw there stuns slows and fears on you and they will do nothing.When they are escaping use your Undertow and you will slow them.Try to take the kills with Reckless Swing.Every time when you fight use your Vicious Strikes it gives you damage and life steal so when you are on low health you can just go to jungle or lane use Vicious Strikes and you heal your self.
FARMING
Ok so farm with your spells try to throw you Undertow and hit all the minions in the minion wave.You will also yous Reckless Swing on some minions on low health but always look your mana because Olaf dose't have much mana so when your enemy use an ability you use an ability.And plus i forgot to say use Vicious Strikes on minions and on turrets they give you damage and life steal.
Creeping/Jungling
So you can take from the Jungle the blue buff and the red the red is not that important as the blue you have low mana so after you level 6 or 5 you can always take blue buff and push the lane very fast.And always try to go top lane.You can take Dragon solo very easy when you have Berserker's Graves Frozen Mallet and Atma's Impaler.

Pros
1.You have a spell that deals true damage Reckless Swing.
2.You have a spell that gives you life steal and damage Vicious Strikes.
3.You have a slow spell and that deals damage and you can push lanes with it Undertow.
4.You have a perfect attack and escape spell Ragnarok.
5.You have a passive that gives you attack speed.
Cons
1.You have a spell that deals damage to your self Reckless Swing.
2.You need to use your ulti very fast and wise because it last for few seconds.

So the you have more Pros than Cons and that says something.And btw you can steal kills very easy with your Reckless Swing.

BERZERKER RAGE
For each 1% of health missing,Olaf's attack speed is increased by 1%
UNDERTOW
Olaf throws and axe to a target location,dealing 50/90/130/170/210(+0.5per attack damage)physical damage units it passes trough and slowing them by 24/28/32/36/40%for 2.5 seconds.
VICIOUS STRIKES
For 6 seconds,Olaf's attack damage is increased 7/14/21/28/35 base damage plus 1% of his max health.While active Olaf gains 9/12/15/18/21% lifesteal and spell vamp.
RECKLESS SWING
Olaf deals 100/160/220/280/340 true damage to his target and inflicts 40/64/88/112/136 true damage to him self.
RAGNAROK
Active:for 5/6.5/8 seconds,Olaf is immune to disables and reduces incoming damage by 20/30/40
Passive:Olaf has 10/20/30 increased armor penetration.

How to play him in early game mid game and late game
Early game
In early game Olaf is very good so you will play him more offensive and you will stay in lane until you destroy a turret or until mid game comes.Try to kill the champions in your lane or just attack them until they have low health so they will go back to base or at list one of them because if one of them goes back to base it will be very easy to kill the other one with you partner in lane.But if you play solo top Olaf you will just play defense and just throw your axe and stay at you turret.
Mid game
OK mid game you will have to start to gank in other lanes you will kill the dragon in mid game solo you will always need to have blue buff so your mana regenerates until you kill someone from one lane to another.But if you stay in lane in mid game you will need to play more defense.
Late game
Late game if you have a lot of minion kills or champion kills you will be op in late game and you will just play offense but don't think if you have are the strongest in the game that you can go 1vs3 or more.Maybe you can go 1vs2 but its risky.
You will only make black cleaver if your jungler is a tank like amumu rammus or something ells if your jungler is offtank the you need to play olaf more tanky.If you go solo top you need to play olaf with teleport it will help you more.The second guide is more tanky and its for solo top.I will update more about the jungle olaf but just to let you know start at blue buff with a pull the try to kill everything in jungle the go back and start ganking.The 4 build is a little of a troll build so play it with a partner in lane.The 5 build is a totally troll build and don't play it more often because you may get a report