1v1: Blind Target/Ignite if applicable, Reckless swing, Pop Vicious Strikes, spam reckless swing, spam Vicious Strikes. (use ult when in need or chasing into towers/groups)

1v?: if you know you may or are running into a group single out squishies with the least escape capabilities. Example Annie, she can only stun you, but your ult ignores stuns. run after her and smash her good, move on to your next target.

Olaf is at home in the jungle. Start off by taking your time to kill creeps, this may take practice on golem spawns and the wraiths. I recommend tackling 1 golem at a time or attacking the lead wraith and backing out to heal before coming back in during levels 1-3.

If you get a lot of crits early game you may even be able to continuously farm, don't be afraid to blue pill often early game.

With Viciouse strikes, and crits you will down those creeps moderately fast early game, and then super fast at around level 4. Use your Reckless strike often to increase your speed and to down creeps faster.

While Olaf is awesome on his own, setting up a gank is always welcome. Coordinate with your team. Let the tank or disables do their job before you rush into a group fight, and if you see a straggler don't be afraid to separate him from the safety of his group and murder him.