What is the quest you need to do in order to finish Fallout New Vegas and where do you go to do that quest

There are four endings depending on which faction you support. You'll be presented with the four faction quests, you can complete multiple missions from each but at one point they will lock out the other choices, or force you to use the Yes Man path. The main quests and their ending quests are,

The House Always Wins - support Mr House's bid to drive the NCR and the Legion out of the region. Final quest = All or Nothing.
For the Republic - support the NCR to destroy the Legion and gain control of Hoover Dam. Final quest = Eureka!.
Render Unto Caesar - support the Legion in defeating the NCR forces and conquering the Mojave. Final quest = Veni, Vidi, Vici.
Wild Card - remove Mr House and strive for an independant New Vegas with yourself pulling the strings. Final quest = No gods, no masters.