Okay first off, this is a late game off tank build. This is meant for survivability and dps. This specific setup is good for all game types, and the items are easy to get as long as you are able to farm properly. You have a high amount of health, coupled with good health regeneration, armor, and attack speed. If needed you can replace the aegis of legion with a guardian angel late game for increased durability and survivability, but you will be getting rid of the damage buff the aegis gives you. This build is great solo lane or in a solid team fight, if your team is there, don't be afraid to run in and do some major damage!

While Olaf is an attack speed/health based champion, adding some regeneration and armor penetration is a good way to show your enemies who's boss, at early levels with these flat addition runes, you gain a significant upper hand. I start off with 9 armor penetration marks, 9 flat health regeneration seals, 9 flat attack damage glyphs, and 3 flat attack damage quintessences. Having this at the beginning and end of the game will definitely teach your opponent's who's the real boss.

For your mastery page, it is good to have added attack damage, attack speed, and armor penetration, along with a little mana regeneration so that you can keep your skills coming, even when your not supposed to. For this I go with a basic 21 points in offense, and 9 points in utility.

In offense I grab attack damage to minions and turrets, armor penetration, attack speed, life steal, and summoners wrath, so that my spells are pumped up a bit.

In utility I grab mana regeneration, Summoner's Insight, movement speed, and death time reduction.

Utilizing your utility tree will make your enemies cower in fear of your superior domination.

Getting boots of speed and three health potions at the beginning of the game is basic for any dps champion.
Right after though make sure to pick up a good health item to utilize Olaf's survivability in lane. Also remember, the more health you have, the more times you can use his oh so deadly E skill.
Making sure you use his dps to your advantage, getting a phage is great choice for a opening item against your enemies. Whether you are pushing or defending, this item is great for it's ability to slow the opponent.
Next, the wriggles lantern, this item is great for dps against minions and jungle, it gives you the ability to do extra damage to minions or monsters, and gives you a good amount of armor and life steal.
Moving on, turning your phage into the big bad frozen mallet is a must, given it's high attack and decent amount of health, it's a must have item for this champion.
The last few items are pretty self explanatory, the aegis of legion gives you health, armor, magic resistance, and a decent attack damage buff, this is a great item for staying in lane against multiple enemies for a longer period of time.
Warmogs armor gives you a boosted amount of health and survivability along with health regeneration which also ties into the runes selected for Olaf.
This coupled with a soon to be atma's Impaler will teach the enemy team that your nothing to fool around with.

It's best to grab your Q at level one, this is because it has a slow and deals damage to multiple enemies at once. That along with a decent amount of range makes it the best choice in any game type. Make sure you have two levels in this skill before reaching level six.
Grabbing your E skill second is great for doing true damage to tanky champions that just don't want to give up. I suggest grabbing this at least two times before level six.
Get your W skill only once before you get to level six, it is great because of the buff and the life steal, but not as needed as your other two skills. Proceed to leveling up your skills by following the guide above, and you'll have no problem out skilling your enemies.

I generally get exhaust because of the damage and speed debuff it puts on the enemy. This paired with either flash, for easy escape from a large group, or a strong fed champion, or ghost, will let you rule the field with an iron fist.

Olaf is a great team champion, his ability to aid in kills and ganks is at top rank in his class, with the ability to do a massive amount of dps along with the ability to slow multiple targets, he can be quite a useful tool in any game type.

Using this build gives you a decent damage output coupled with a high health level. With his ability to heal both health and mana, along with the ability to do increased damage to monsters, he proves to be quite useful to any team that he plays with.

While farming with Olaf, I suggest to use your axe to last hit multiple enemy minions so gold is easier to obtain. Make sure to actively pick up blue and red buff whenever you can, and don't forget that you have a lot of health and defense at later levels, use it to your advantage.

Here's just a look at what can happen when you build this way, a good amount of cs, nice champion kills, and only 1 death along with a few assists. There are multiple proof if you aren't sure. I did however replace the aegis of the legion with a guardian angel, which proves to be the (upgraded version) of that item.