Im making this guide because Olaf is op and I'd like to share it with you. I am motivated to make this guide because Riot has buffed lethality, pushing Olaf into the top tier category again. He benefits from almost every fighter item and has a great passive and ult passive. He can lane against anyone and he has a perma-slow with natural life steal. Easy to play and snowballs fast. Iv played this game for 6 years, Olaf has always been there for me when I needed a go-to top beast. I mourn for the days when his ult gave him passive armor pen. My summoner name is DYEL99 I don't play ranked anymore but I have played this game since almost the beginning.

use the lethality runes. Since it got buffed to 60% base effectiveness you can tear through any enemy. Starting the game at lvl 1 you have 32.5 lethality, that is 20armor pen. Your opponent has 6 armor if he is using the armor seals. Thats basically true damage. Trust me on this you are going to love it.
I know i know, he benefits from AD runes on two skills, however 15ad is super cheap compared to getting 24 lethality. AD is so easily obtainable and cheap its not really worth the runes IMHO.

Start with dorans sword for health and damage, the two things you only need, due to huge armor and mr from ult passive. Deaths dance first. Always. Gives you heal from tow and reduces damage by 15%. Not to mention some nice cool-down. A very effective item on olaf. This will keep you in lane and in fights.
Health next, i usually get t-hydra because its a nice balance and push power increase. Stacks with Deaths dance nicely when engaging many enemies.
Next get Maw if there is a magic champion that is wrecking face, if an AD champ is giving everyone the works get thornmail, allowing you to win ever duel. If you get Thornmail, get mr boots. If you get maw, get armor boots. The next items are up for interpretation, because they are all completely situational. Frozen mallet is a good choice because it increase the slow and gives you Health and AD, the only things you need.
Dont get triforce, you dont need atkspd and its a waste of money for you. Focus on building health and AD in bursts.
Black Cleaver is useful,some people get it, however i find it overly expensive and the health isnt enough for me, plus you already have 20-32.5 armor pen at the beginning.
SPIRIT VISAGE. Very useful for olaf, covers your health problem and boosts your life steal and W. However... doesn't contribute to damage, get this item if you are behind against an ap-stacked team.

Undertow first for harrass and farming potential. Obviously get R when available. try to build e and w at the same rate, since they act synergetically in combat.

Engage with undertow, run to the opponent and use E, try to pick up your axe when you do this so you can throw it again if he tries to escape, then hit once for T-lords damage. If he decides to engage you, use the W when below 50% health, make the enemy think you are losing then come up on top with a massive heal. If your enemy does not want to engage when you hit the T-lords run to the axe immediately and throw it again to keep him near you for damaging.

Never engage with your W. You will ruin the attack for yourself. W is the "oh **** button". It works well when low life because your passive grants you additional atkspd.

Flash is very useful, get it everytime. Teleport too, stay in lane and gives you split push potential. You dont need ignite and you don't need ghost, your undertow will provide a perma slow so that you can stay engaged for as long as you'd like.

Farming is your secondary priority behind staying alive. Undertow is great for nabbing those far away minions. Try to hit your opponent with undertow and kill creeps at the same time, that way mana is not wasted and you gain an advantage in lane.

PROS
+You don't need atkspd
+passive armor and magic resist
+can't be cc'd
+True damage for tanks
+Slow and natural life steal
+AD champ with a projectile, very unique
+all-around effective, high utility

CONS
-if you use ult too soon you will perish
-needs health to engage people
-if you aren't attacking someone in a teamfight you are going to lose
-people always run from you, no one wants to engage.