1.Gromp-Use Smite when it first spawns
2.Blue
3.Wolves
4.From here, you can either invade or head to the Raptors.
5.Red-Use smite when your W is proc'd
6.Golems
7.Gank or back

1.When attacking gromp, smite it as soon as it spawns so the player that is leashing knows when to leave and it's just better to have the buff going. Also just stand between the wall and gromp to throw your axe and it'll pick it back up again automatically.
2.When fighting blue and wanting to come out with a bit more hp, use your W on the small minions and then attack the blue monster last and when it's around 650hp your W will come up again and activate it once more. You'll end up with more hp than going straight for the blue.
3.Attack the big one first and you're fine.
4.I personally like to invade because olaf has such a strong early game. Just make sure that your team knows. If not you can do the raptors.
5.When attacking red buff it's best to smite it when your W is proc'd due to the fact that it's passive has an increased healing.
6.Attack the big one first and you're fine.
7.At this point you should have 2 potions. If you want to gank you can activate your W and consume a potion for more healing or just back and get your items.

When ganking a lane, you want to use your chilling smite first at the enemy champion. The next step is to do what Olaf is known for the Pain Train. You pretty much throw your axe at the targeted enemy and pick it up, then throw it once more and repeat this step till they die. :)

This video is a great example of the pain train. PainTrain