Basically you need to retrieve the type of staff mentioned by Neloth and return it to him. Annoyingly, the location of the staff can be random, but below are lists of both the most likely name for the staff and the areas in the game you’re most likely to come across it.
Skyrim is the homeland of the Nords, a fierce and proud warrior people who are well suited for the bitter cold and mountainous terrain which defines the land. Now scarred by civil war, Skyrim faces its darkest days with the return of the legendary dragons and their leader, the World-Eater Alduin. The future of Skyrim and even the lands beyond hangs in the balance, as the people await the prophesized Dragonborn, a hero born with the power of The Voice and the only one who can contend with the dragons. You are that Dragonborn; your task is to investigate why the dragons are returning, and discover a way to defeat them. At the same time, you’re free to explore Skyrim at your own pace, uncovering its many wonders along the way.