Not Updated For Current Season
Olaf is very tough. With a big HP pool his reckless swing can do immense damage and olaf can survive a fight easily.
His first item is Manamune. With this you will always have mana and 2% of your total mana is coverted to damage and it grants you a lot of damage.
His second item is Mercury's treads. With this you can survive teamfight's and 1v1 figths if you are low on HP. It grants you 25 magic resist which is also good.
His third item is Frozen mallet. This will give you a lot of HP and some damage but the most important is the slowing effect. You don't need to hit the enemy with Undertow, just auto-attack him and the enemy will be slowed.
Atma's Impaler. The most important item. It will give you a lot of damage because of the item's effect. 2% of your HP and 2% of your Mana is converted to damage which will bring you above 300 damage.
Banshee'S Veil. It grants you 450 HP, 400 Mana, 57 magic resist, 17 damage (Manamune and Atma's) and a spell shield. All of this item's stats is good for this tactic.
Frozen Heart. If you are fighting with a DPS or you are in the middle of a teamfight it will bring down the enemy champion's attack speed. It also grants you 25% CD reduction which is good for your Reckless Swing. Frozen Heart will also grants you 10 damage because of Manamune. 99 Armor is very effective too.
Ghost: Ghost and Ragnarok is a big combo and you can survive teamfight's easily.
Ignite: It's the best spell against lifesteal. With this DPS champ's will not have any chance against you.
I do not prefer any other summoner spells but you can pick any other if you want.
Playing with Olaf:
This build prefers late game so in the early game play a bit defensive until you have Frozen mallet. You will not have so much HP regen so you can use vicous strikes if you want some HP (you can use it anytime because you have Manamune). When you started ganking you are important in team-fights. You will be the only meele who can do a lot of damage and can survive anytime. If you have a good CC team against (ex. Amumu, Morgana, Galio, Warwick, Miss Fortune) you are the best against them. Just run in use Vicious strikes then use Ragnarok and spam reckless swing on somebody. Try to last hit with Reckless Swing on the enemy champion's (bonus gold but makes your team a bit angry) but if you are doing great they will forget it :P.
Be very useful for your team:
If your teammates are newbie's help them by telling them what is Baron, Lizard and Golem buff. Help them killing the Lizard and the Golem. Try to kill Baron every-time it spawns because his buff is a great advantage and with olaf you can easily tank him to help your teammates. Try to get all the buff's on the map (Lizard, Golem and Baron) and always kill the dragon (you can kill the dragon alone).
This is MY opinion so it isn't the best build but I love and it's very strong too.
Please add some comments and write down YOUR opinions. Sorry for the grammatical mistakes.
Thank you for reading!