This is recommend to max it first for this reasons:
It has a good damage output, sustained and few explosive.
The skillshot don't reduce his power by enemies hit.
Compareted with others skillshots, it haves a big missile width and doesn't have additional mana cost in high ranks.
It has a low cooldown and can be reduce itself.
It can be use to explore the fog of war.
Most of the times try to recover your axe, even in a battle and specially in early levels, where it shines much better.
Try to land the axe in the same place of your objetive, this will allows to chase him, lets refresh its cooldown much quicker and increases its slow uptime.
The axe will remove the fog of war in a large area around when it lands in the ground for a very brief duration, making it useful for checking bushes.
Aditionally if it dont's reveals enemies, try too listen the sound effect when it hits them.
When jungling, use the stick function to your favor, put the monster between Olaf and terrain, in this form the axe will lands more close to Olaf, with some practice the axe will be picked without going for it, like in old patches.
Provides complete immunity to all forms of CC, and largely defines Olaf's playstyle during the later stages of the game. It can be used either to initiate a battle, to improve his fighting ability midway through one, or to make an emergency retreat if the situation starts to become disadvantageous.
Olaf's most common and effective role during late-game teamfights is to function as a bulky assassin. Upon the commencing of a pitched teamfight, Olaf can activate Ragnarok and dive straight through the frontline of the enemy team, singling out the opposing AD carry. Because of the complete CC immunity that Ragnarok affords him, he becomes extremely difficult for the opposing team to peel away. Even if Olaf is unsuccessful in slaying his target, the threat he poses is often enough to drive them completely out of the teamfight in their attempts to avoid him, drastically reducing the enemy's team's damage output.
Olaf is also a very useful peeler himself, operating to safeguard his own carry from the opposing team. His ability to chain-slow enemies with Undertow and the excellent damage output from Reckless Swing can make it extremely difficult for enemy champions to safely attack the carry without risking being kited and killed.
Olaf naturally receives armor and magic resistance from the passive effect of Ragnarok. Because of this, it takes more effort to kill him, therefore stacking health on him is a very common build path.
Consider Warmog's Armor or Frozen Mallet if a build with one sole healthitem is desired. Frozen Mallet is one of the most useful items for Olaf, as in addition to the large amount of health it has, it slows any opponents he autoattacks, giving him a much more reliable form of crowd control than his Undertow. However, if the player is confident with their ability to consistently land axes on a fleeing opponent, then Frozen Mallet can be substituted for a Warmog's Armor for its much greater health and survivability boost.
Titanic Hydra is an excellent option for Olaf because he will usually stack a lot of health late game, making Titanic Hydra'sCleave passive very attractive. Olaf does not need the lifesteal from Ravenous Hydra because he can already gain lifesteal with his Vicious Strikes. However, purchasing Titanic Hydra during the early game is not recommended as you need some health to make this item's passive (and active) worthwhile.
When Olaf does not have Ragnarok or Undertow available for use, he can be extremely vulnerable to kiting. A Randuin's Omen greatly reduces the effectiveness of this tactic and also offers a considerable amount of health and a useful active slow which Olaf greatly appreciates.
Dead Man's Plate can be considered an alternative to Randuin's Omen in a more offensive oriented build, as it also provides movement speed, situational damage and sticking power from the Dreadnought passive. However, it is recommended to build at least one AD item component such as Phage or Hexdrinker before completing Dead Man's Plate, to ensure that Olaf can actually deal enough burst damage once he gets to his target.
Spirit Visage is one of the best items Olaf can purchase. It synergizes with Vicious Strikes, increasing the sustain that is already increased by the ability itself even more, not to mention any lifesteal item that Olaf is likely to purchase. The cooldown reduction is also a great asset to Olaf. Due to these reasons, this item is nearly essential for Olaf, except when there are no AP champions on the enemy team.
Olaf does not need Banshee's Veil that much because Ragnarok makes him immune to nearly every crowd control he would want to block with this item. However, it should still be considered if there is an important damaging spell that Olaf should block.
It is important to note that Blade of the Ruined King deals damage based on the enemy's current health. Generally, enemies want to stack health to mitigate the effects from the true damage dealt by Reckless Swing, but since Blade of the Ruined King counters this, there are very few things in terms of defense that enemies can do to mitigate Olaf's damage with this item. However, if offers lower raw AD, therefore less damage with both Undertow and Reckless Swing itself. The extra attack speed and the active from Ragnarok should compensate for that, however.
Heavy cooldown reduction also greatly benefits his Reckless Swing - with access to at least 284 true damage nuke on a 4.8 second cooldown at level 9, Olaf has excellent damage output from it alone, allowing him to dedicate the rest of his build towards improving his defenses and tanking ability.
Olaf has no dash ability, so augmenting his mobility with early boots upgrade often proves to be very effective.
Olaf does not need armor penetration. When choosing between flat damage and armor penetration, it is better to go for flat attack damage because his main target is the AD carry with low armor and the true damage from Reckless Swing deals decent damage to tanks. Undertow also benefits from flat damage. If the enemy team is especially heavily armored, The Black Cleaver is still a reasonable purchase though as Undertow spam and basic attacks can quickly shred the entire enemy team's armor.
If your team plans on killing Olaf, fully commit in doing so. Leaving the job-half done will make him even more dangerous due to Berserker Rage and he is likely to simply life steal all the damage your team did to him.
Undertow is a slow projectile, meaning that you can dodge the spell easily.
You can deny Olaf from spamming Undertow by keeping him from picking up the axe that the spell left in the path.
In a similar vein, making significant course changes while Olaf is chasing you will prevent him from picking up his axe and continuing to close the distance on you.
Save your CC while Olaf is using Ragnarok. It removes and negates any CC cast on him while it is active.
Olaf'sRagnarok also gives him bonus armor and magic resistance. However, when activated, the passive bonus is lost and he gains a lot of AD to boost his damage. It might be wiser to try and burst him before the buff duration is over.
As Olaf is immune to any forms of CC placed upon him, the most effective forms of keeping him away are self-displacement abilities such as Arcane Shift and player-created terrain such as Cataclysm. You should try to save these abilities for when he uses Ragnarok to make him waste the duration.
Keep Olaf from reaching your team. His high auto attack damage and high lifesteal from Vicious Strikes can easily take out most of your team with full HP if Olaf is left overlooked.