This is my first build so hang with me, I might not describe everything like I should but I do what I can. And don't forget I'm not that high of a level yet so change runes and masteries to how you personally think would work.
It didn't take me long to find Olaf in the champions section and realize that I wanted to play him. He is an amazing dps, anticarry, and if played right an epic carry. After trying out the higher ranking Olaf builds I realized that how the builds just weren't suiting how I wanted to play. So I started to build my own in some bot matches when I realized that Olaf could be played as a tanky-dps but overall he showed his true potential as an allout rip out their hearts killing machine. This guild shows how I do that.

Pro's : Amazing DPS, Godlike EndGame, good harass start game, Great Anticarry, Great Survival capabilities, Can kill most champions one on one if played right.

Con's : Slow StartGame, Only CC is a slow, If you get lock downed its hard to bring him back.

I'll admit runes aren't my strong suit - I think you should go with whatever you feel is best but I like to get the extra armor pen. (stacking with his ult's passive you might be able to get true damage for every attack if they don't build into too much armor) and some armor and magic resist just so I can live through the punishment.

In masteries again it depends on how you want to play, I'm an aggressive player so I build into lots of attack and if I'm not careful enough I'll die so Good Hands is great for me. Especially because Olaf doesn't have really any crowd control except his slow on Undertow.

I always start with a Vamp. Scepter because you are going to be taking some damage and it really works well with his Viscous Strikes. The greaves are obviously just for the movement speed and attack speed. Stinger I use mostly at start/mid game because the attack speed and cooldown reduction are worth the low cost, but end game go ahead and sell it for whatever you want. The phantom dancer is great for Olaf because he thrives with attack speed and crit and the extra movement speed is just giving you that extra push to finish off a fleeing enemy. Depending on how you play Stark's Fervor could be substituted for the Bloodthirster but if you aren't careful and die a lot use Stark, in my opinion its the better item because Olaf can do enough damage with attack speed than the extra from damage from bloodthirster and it also will help your team fights. Once you get infinity edge go ahead and be cocky you can take down most champions in one on one and sometimes two on two if your smart. Even still be careful, you don't have to worry as much anymore but still be ready to run if it gets tough. After this anything you get is just icing, the extra phantom dancer makes you even more powerful and if you switch out the stinger for a health item (warmogs or Frozen Mallet) then you could solo Baron if you play right (done it once or twice in bots but haven't managed to get enough money for my stuff in pvp yet cause it always ends too fast lol).

Important: If you'd like do have build him more of a tanky dps I'd Start off with Greeves, then move to either getting the Atmog's combo or Thornmail (assuming the other team is AD heavy, I always grab this if they have a Tryn) and Frozen Mallet, (Spirit Visage can work well also because of the increased healing to yourself). Replace those for one of the P. Dancers and Stinger.

So how I play Olaf is:

StartGame : Grab your Vamp Scepter and Undertow and go out bottom or top (if your laning with someone with good CC's then you can get some nice early kills). Do what you can to farm minions and harass with Undertow whenever possible. Be ready to take some damage and remember to dodge skill shots. Play carefully, that doesn't mean hug your turret just don't overextend and kill get yourself killed. When you have enough money (usually about level six) go back for your Greeves and a dagger if you have enough. Don't start ganking you don't have enough attack speed to do enough damage quick enough yet, go back to the minions and keep farming your gold. Once you have Stinger you can start focusing on the champions in your lane, Start with your Viscous Strikes and Undertow, grab your axe back up for the cooldown reduction and smack them with Reckless Swing, after that you can just keep repeating whatever comes on cooldown first. IMPORTANT: do not waste your life chasing too far if they run and another is still attacking your lane-mate go kick his ***. Go back and build Zeal when you can and another dagger, then stay in lane until you get your Dancer. With that you can start doing some serious damage but still not enough to be overzealous, next is Stark's Fervor which can save you and your teammates ***es with that lifesteal and attack speed. Once you have it go ahead and grab blue buff (and red if you like) and start setting up some ganks for some fun. Don't only gank take down your towers also its an obligation. Keep doing this until either you win or the you have all your items if you do, go ahead and try to take Baron, it will be a close fight but if you are playing right he should go down, IMPORTANT : This is NOT needed its for gloating rights and to watch Olaf do what he does best, if you feel like you are going to die do not do this, if you get low run, do not pop your ult first thing if you do attack. Thats About it you'll get a hang of him otherwise yourself, remember don't be an *** to your team or the enemy team its not needed it ruins the game for some people. And always Good luck and Have Fun.