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Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Alrighty, Olaf is fairly new but for anyone who has played him or played against him has seen that he is somewhat like tryndamere in the fact that he becomes significantly more dangerous the lower his health is, so my build is based on a good amount of damage and vamp, not so much attack speed since he gains enough with the runes + boots + his passive.
So to start off, i like to grab a ruby crystal because the health early game will aid your vicious strikes, and the percentage that goes toward your passive will be better with you having a bit more health.
Berserks greaves are nice for your early game because they add a little dps and paired with your runes you can get your attack speed up there pretty nicely to start off. These, however, are a bit more useful end game with the item build.
Frozen Mallet is always a good idea because the hp boost helps significantly (seems to be a pattern here) and the slow will help you chase while undertow will let you close any gap they are able to create.
Now, i choose to get the bloodthirster before my last whisper because when you are low enough on health in a fight, your passive will grant you that attack speed you want, and a bloodthirster + vicious strikes has kept me at about 10% health many many times, allowing my attack speed to be quick enough to keep my health there and let me finish off whomever it is i am dealing with. This is definitly a tactic that takes some getting used too, but if you stick in there and dont run out so you can life steal, you will survive through it and pull some insane dps.
last whisper is nice because the attack speed will top your passive off a bit quicker, and you can really be an end game tank killer with the armor pen + reckless swing. Plenty of times ive blown through a Rammus's health in a flash because of that combo.
Early Game Olaf is not a great early game champion, he can do some decent damage but the short length of his abilities doesnt allow him to stay in there too long. Undertow is used a little more defensively in this phase but any chance you can use it to close the gap for a kill do so. THIS ABILITY IS NOT MEANT TO HARRASS. I have seen many people try to harass with it, and it is a huge waste of mana.
Mid Game This is the point where the other team is really starting to be a bit scared of you. At this point you should have enough of your items to keep yourself in a fight without worrying about getting kited/outnuked, and your ult can really keep an enemy attacking you thinking that you are close enough to death. Your ult is something you want to use when you are lower on HP because of the damage reduction to keep your enemy on you so you can pump out that dps. That paired with vicious strikes will keep you at a comfortable place in any 1v1 or even 1v2.
End Game Now end game is when you should be the 2nd person into a eam fight (assuming you have a tank) and while most champions avoid attacking the tank, that is your bread and butter. being the 2nd in you will usually be the target of 1 or 2 champions which will get your hp low enough to kick your passive in, and a couple reckless swings paired with ragnarok will do the job a lot quicker than expected. An exhaust is useful here to keep him from escaping, as well as ghost if necessary.