Upon getting Tiamat, it is smart to jungle quite for a little while to get the money needed for Stingers. With Nocturne's passive ability with Tiamat, you will be able to easily kill minions and monsters in the jungle.

+Pros+
+Fast attack speed, so minions/monsters die faster and you can land extra hits on champions.
+Wider range of attack, meaning you can hit many more monsters/minions at once.
+Can deal 100-200 extra damage to champions, minions, and monsters using Tiamat's active.
+Can move extremely fast, especially when paired with Duskbringer.
-Cons-
-Doesn't deal as much damage as it possibly could.
-Can be a bit squishy early-game.

With Tiamat, you get two skills. One is passive, and the other is active. The passive skill will cause a small AOE type attack that will deal 20-40% of your Attack Power as damage. The active skills functions the same, except the damage is changed from 60-100%. You also don't need to be attacking anything to use it, meaning it can be good for attacking escaping champions (or when you need that little attack boost).