I take this items so I don't have too low health and I do heavy damage. I'll make a list with all the reasons to take these items.
Frozen Mallet, for the additional health and the slow on basic attacks.
Berserker's greaves, It's for the additional movement speed and attack speed.
Phantom Dancers (2z), for the attack and movement speed.
Blood Thirster, for the attack damage and life steal.
Infinity Edge, for the additional damage when you critical strike someone.
If you have problems with a tank against you, you can buy Madred's Bloodrazor and place it for a phantom. Why? Unique Passive:
On hit, deals bonus magic damage equal to 4% of the target's maximum health,(max 120 versus monsters).

I build Olaf as a AD fighter. I buy Frozen Mallet for the slow and the additional health. Health's just for staying alive in team-fights. Of course I buy some Life steal to get extra health when farming and winning fights easier. It's very important to last hit so many minions as possible to receive some extra gold. I recommend to go solo top in 3 vs 3 and try to go solo top in 5 vs 5 to for more minions for yourself. When there's no one who jungles, you have to try to lane with a support who doesn't last hit. When you're build up, you can sell your berserker's greaves and buy a phantom dancers.

I take this Masteries for almost every DPS champion, 21-9-0. The AD in the Offense tree for just more damage and the extra armor in defense for some less incoming damage. Olaf's ultimate gives armor penetration and that stacks nice with my masteries.

I take Exhaust and Ignite. Exhaust for two reasons:
One, to slow your enemy who almost came away.
And two, Exhaust reduces the enemy's attack damage for 2,5 seconds. That's very nice against other AD champion. And I take ignite to finish champions how try to come away. If you don't want to tank ignite, I'd take ghost to keep close to your enemy.

I always take this runes for the more attack speed and damage begin game.

I always start of with my Q ability for the slow and damage for first blood. Then I train my W and E ones, and start of training my W full time for the life steal. And I always train my R when possible.

Only give a minion a first hit and then wait until he had less health as your damage. That's the easiest way to kill minions.

You're the one who suppose to do the most damage in a team-fight. If your has a good tank, you can stay alive and do damage.

Thanks for reading my Olaf guide. Please like for more guides and leave a comment with an other champion who you want me to review.
Good Luck and Have Fun with Olaf, The Berserker.

Why is First Blood so important? The additional gold you get with first blood is necessary for the development of the game. The extra gold makes Olaf much stronger and you do much more damage. Before you go, think of these three steps:
Look at their Summoner Spells, 2 or more heals, don't go.
Look at you enemies, are they OP, like Tryndamere, don't go.
Is/are your teammate(s) going with you, no?, don't go.
And last, but not least, do you think you got a chance to win?, no?, don't go.