Build Guide by Lamorak#14224
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The overall idea is to be continuously building HP throughout the game while complementing it with some armor and magic resistance pausing only to get the Impaler to complement Olaf's awesome passive after which I go back to stacking HP until the game ends. I level Swing and Undertow early-mid game for my damage and farming and then Strikes late game when I have the HP to back it up. In the end I'm (ideally) left with an Olaf who is beefy and dangerous from start to finish in the latter of which he becomes god-like :)
For skills I prioritize Reckless Swing (because of its huge damage early-mid game) first, then Undertow (because of its Olaf's farming skill and does good damage early-mid game), and Vicious Strikes last because it scales with your health which you have the most of in the late game. Ragnarok, of course, I level whenever available. As for the items listed, I like to start with a Ruby or boots building into the Heart of Gold ASAP (to max its gold-yield) and Greaves ('cause they're cheap and good for any melee champ) followed by Spirit Visage. Then I go straight for the Impaler (selling the Heart of Gold in the process since its armor becomes redundant with the Impaler) to give Olaf even MORE damage per health boost, and then I just start stacking health items until (if the game lasts that long) Warmog's comes in view.
I find that I can be quite aggressive from the very beginning because I have more health and resistances than my opponents from the start. I shamelessly spam Undertow both to soften up champs for ganking and to farm the minion wave. Throwing the axe as far as it will go every time is usually not a good idea because Undertow is only spammable if I can retrieve my axe. Once softened, I can confidently slow, charge, and "Reck" my target. Usually I've taken or soon do take some damage so my attack speed quickly ramps up to the point where nobody wants to mess with me up close, and Undertow+Swing ensure that they can't go anywhere else. Mid-game I'm a decent initiator because I'm durable, but can pack a punch fast with Swing and either ult back out or ult to stay in and keep causing havoc. Once they run, Undertow makes for easy ganking. By late-game I'm a fully-fledged tank with huge damage potential. I can charge, Reck my target, pop Strikes, and chew through them at lightning speed.
I like clarity because it will allow you to spam Undertow to your heart's content which is essential for farming, harassing, and lane control generally. Ghost, of course, is an essential which EVERYONE should have available at all times. It's great for getting away. It's great for catching up. It's even great for getting back in your lane asap after a respawn (which is practically the ONLY thing teleport is good for).
A note on Trees and Runes
I tend not to care so much about Tree building since the cooldown reduction skills are the only reason I like the Trees and it seems that they are glitched and don't work. So by all means pick up your extra 6-points of armor or damage or whatever, if you like. Runes I care even less about because I don't want to pay real money (which is what I would have to do to get any number of them) to get +2.23% crit damage or something. However, if you're into this, get what you like because so far as I can see pretty much any stat you get with Trees and/or runes will be useful regardless of your champion. Ultimately, I just care about skill and item building as those make the biggest, most direct impact on any given champion's success or failure and are VERY champion specific.