Hello summoner. I'm Trüesteel and this is my Olaf guide. In this guide I will recommend Runes, Masteries and Item builds for Olaf and try to give you some useful tips.

Pros
Great damage output with survival.
Can fight and win on low life.
Great jungler and solotop.
Great chaser.
CC immunity and ability to break out.
Great 1v1 and even Morev1 is fed.
Has Trüe Damage to burst down squishies and even take on tanks.

Cons
Does not benefit from AP.
Has next to no harrasment with Undertow.
Has next to no CC with Undertow.
You will feed if you rambo.

Armor Pen reds.
I take them because combined with Ragnarök's passive it gives me an edge against all my enemies and in most cases saves me from using a slot to counter armor.

Defense yellow and blues.
Pretty self explanatory. You can take hard blows and repay in kind.

Health quints.
Well, armor pen or attack damage would also go well with Olaf, but I prefer early game tankyness and considering that Vicious Strikes gives bonus damage based on health it not a bad choice.

19/11/0 has served me well for solo top Olaf. It gives all the attack damage per level and survival ability I need. For Jungle Olaf I usually sacrifice defense masteries for more mobility and extended buff durations.

Laning
If you're laning you'll probably want to be solotop. You can dominate almost any champion 1v1 and just heal yourself with your W while making money. Basically what you'll want to do is just get last hits. But if your oppenent is getting agressive, you should repay in kind. Don't worry you'll be alright unless you do something stupid. Just slow them with your Q then pop W hit 'em a couple of times and smack 'em with your E. Repeat if you think you can take 'em. When your jungler comes to gank, just take your time with the axe throw and with your summoner spells you'll be able to get a kill out of it.

Jungling
You can start with either Armor and pots or a Vampiric scepter. -Use your Q while W is active so you can get more HP back-. Both works fine on Olaf but I'd recommend the armor and the pots because you can rush your razors faster and that help you both in the jungle and on ganks. Your route would be Blue/Wolves/Wraiths/Golems/Red.
After finishing your path just bluepill and buy boots. They'll come in handy. Now you'll want to utilize that red buff.

Ganking
I must say this part does not completely in your control. Your teammates should've harresed their opponents a bit. You're okay to gank if your pret has 70/75% HP. But make sure your teammates ddon't scare 'em off. Take your time landing the axe. It has a good range. After landing the axe, pop ghost and hit 'em with everything you got. Make sure you pick up the and throw it over and over again. Also see if your teammates can make them burn flash. That way your ganks will be more successful.

Counter Jungling
Olaf is a fast jungler. If you can't gank, you should counter their jungler. All buffs have 5 minute colldown. Make sure your smite is up when trying to steal buffs. And don't try to do it if you think you can't get away with it. Also watch their inventory to see if they got wards. You can see them until they place it.
If you have a run in with the enemy jungler, see if you can take him on. Olaf is great 1v1. But if you see any opponents missing don't risk it. Stealing buffs is only worthwhile if you can get away with them.

In every case you should max your E and W first. Giving a second point to Q will help you chase more effectively though.

Recommended build on top usually makes me a god that can do tons of damage and take a lot of beating. Sequence is mostly up to you but don't rush your mallet unless you are not well farmed and in dire need of survival. Just buy Phage then get some lifesteal and attack speed you need.

Recomended good items.

Berserker's Greaves; usually should be your boots unless enemy team has a sustained CC'er like Ashe with her Q and Sejuani with her passive etc. If enemy team has more CC than your Ulti can handle -which is a rare situation- buy Mercury's Treads or if it is a heavy AD team Ninja tabi can help you too since Atma is more of a damage item than pure survival..

Frozen Mallet; is a really viable option because as a fighter you have to survive fights and deal some damage as well. This item gives all that and with your W some more. You can also stick to single targets after buying Phage.

Phantom Dancer; is amazingly good on Olaf. Gives him attack speed, the movement speed he desperately need and an always welcome Critical Chance. Crits are always welcome because when combined with lifesteal it heals for double the usual amount. Can give you the edge when fighting on low life.

Atma's Impaler is simply a great item on Olaf because it gives you defense, damage and again the critical chance.

Force of Nature; gives Olaf great mobility and magic resist to make him tanky against mages. Can be left out if you prefer Banshee's Veil which is another good chocie.

Banshee's Veil; is also as I said, a great choice. If enemy team has nukers and you want a little bit of more health. Olaf usually does not run out of mana mid-lategame but and early catalyst may help you chase foes with Undertow and survive some tough encounters.

Stark's Fervor/Zeke's Herald; It was always useful for Olaf and it still is. Now it gives less attack speed/lifsteal but more health and CDR. You can buy it if you're not jungling. CDR will help you spam your trüe damage and vicious strikes more. And that extra health give come back as some serious damage.

Youmuu's Ghostblade; is pretty good on Olaf. Armor pen CDR Crit Chance and a godly active with low Cooldown. Ghostblade's active combined with your ulti, passive and W will make you able to win every low HP encounter be it 1v1 or even 1v2.

Bloodthirster; is also great on Olaf if you want more damage with your lifesteal instead of attack speed. Does not need much explanation.

Other items on Olaf

Hexdrinker. Gives you some MR and AD. It has proved useful in 3v3. On 5v5 only get it if you don't want to save up for some more serious items or if you have a fed Karthus as an enemy.

Black Cleaver. Pretty good on Olaf. But I almost never end up buying it because I have enough ArmPen due to Runes and Masteries. Buy it if you want extra damage which in my opinion you won't need unless enemy team stacks a lot of armor.

Wit's end. Meh. Simply meh. A cheap item for some MR and AS but I almost never buy it beacuse I usually can save up for a negatron cloak. Also With Phantom Dancer and Zeke's Fervor combined you'll have pretty efficient AS.

Mardred's Bloodrazor. Actually not a bad choice for Olaf but I never get Mardred's Razors unless I'm jungling and in that case I usually end up buying Wriggle's Lantern for it is more beneficial. Let your carry buy it.

Items you should NOT buy.

Trinity Force. I've seen some builds that include this. Trust me, it is not worth the money. And sheen's Ap is completely wasted on Olaf. Buy something else.

Tiamat. Explaining why seems redundant.

Sword of the occult. Your damage does not come from your pure flat AD items. It comes from a mix of AD and HP. You DON'T need it.

Warmog's. Your Frozen Mallet is much more beneficial. Gives you damage and health with chasing potential. You don't need Warmog for more health.

Cloak and Dagger. It sounds good on paper but you're Olaf. You don't need this item.

I usually take Ghost and Exhaust for spells, mastering both(duh). It is great for chasing foes.

In the case of Jungling however, take Smite and Ghost.

Flash is taken by many, but it is not as beneficial as ghost. I'll explain later on the guide.

Ignite is just meh. Reckless swing is a great way to finish of people. I don't reccoment ignite.

Teleport. Now if you want so solo top without worrying about your turret take it. If is in fact useful. But take Ghost as the second one.

Clarity. No, just no.

In teamfights you are able to roam the battlefield with Ghost and Ragnarök. You should try to kill their carries to take pressure off your team. But if your team is already focused on thier fighter you should join in to chop him down faster. But NEVER use your potential to go after the tank. NEVER.

You should not underestimate an enemy whom has burst damage. They're your worst enemy when on low life. If they don't have burst damage however, just go for it.

Do not go 1v1 on low health against an opponent with CC unless you have your ultimate.

Do not let yourself be kited by Malphite, etc. learn when to disengage.

That seems to be all for now. Thanks for reading please vote and comment. And good luck in your matches.