Matthew 22:21 of the Bible instructs those to "render unto Caesar the things that are Caesar's"; as Caesar sees it, the Mojave shall be rendered unto him after he allies with or destroys certain tribes around New Vegas.
Meet Caesar in his tent atop The Fort and hear his requests.
Destroy the Securitron vault beneath the weather monitoring station toward the back of the camp. There are three generators in the vault that can be shot to be destroyed; destroying them will in turn cause the vault to go into meltdown and explode.
The White Glove Society does not initially seek an alliance with Caesar. He can be told this and he will ignore the group.
Alternatively, the White Gloves will solidify their allegiance to Caesar if Marjorie and Mortimer are spoken too after completing Beyond the Beef and reverting the White Gloves back to cannibalism.
Destroy the Brotherhood of Steel. One can do this by either choosing to kill every member conventionally; by hacking Paladin Ramos' security terminal (Science of 75 required) and setting the bunker turrets to target Brotherhood members; or by getting the three keycards from Elder McNamara, Head Paladin Hardin and Head Scribe Taggart to initiate the bunker's self-destruct sequence.
Travel to Cottonwood Cove and take the barge up the river to the fort.
Speak with Caesar
Accept Caesar's first task
Demolish Mr. House's bunker under the weather station
Return to Caesar
Kill Mr. House
Return to Caesar and report that Mr. House has been neutralized.
Earn the trust of the Boomers and forge an alliance between them and the Legion.
(optional) Kill the Boomer leadership to neutralize the Boomers as a threat to the Legion
Inform Caesar that the Boomers will support the Legions against the NCR.
(If you killed the Boomer leaders) Inform Caesar that the Boomers have been neutralized as a threat.
Bring the Legion's offer of alliance to Marjorie of the White Glove Society
Bring the Legion's offer of alliance to Mortimer of the White Glove Society
Inform Caesar that the White Glove Society won't support the Legion.
Destroy the Brotherhood of Steel's bunker.
Tell Caesar that the Brotherhood of Steel threat has been neutralized.
Meet with Caesar for a private conversation
Speak with Caesar once he's been cured to find out your next task.
Return to Caesar to be recognized for your service
Report to Legate Lanius to begin the Battle for Hoover Dam
Upon receiving this quest, depending on your progress so far, you should have received invitations to the three main factions quests and you will have to make decisions as to which you will support. Proceeding too far down this questline will prevent you from completing the others. For more details see Ring-a-Ding-Ding!.
Destroying the generators will cause you to fail The House Always Wins.
If you become vilified by the Legion at any point during this quest, it will fail and the unmarked quest Beware the Wrath of Caesar! will start.
The Courier has the option to tell Caesar off by saying "I am done working for you." Caesar will give them a stern warning. If they choose that dialogue a second time, everyone in the tent will become hostile.
The name of this quest refers to a Gospel story in which Jesus Christ is asked whether or not the Jews should have to pay taxes to their Roman rulers. Jesus responds by asking whose image is on the denarius. His challenger replies "Caesar's", thus admitting that the Jews are, after all, using Roman money. Christ then instructs the crowd to "render unto Caesar what is Caesar's and unto God what is God's."
PCPlayStation 3Xbox 360 Completing Beyond the Beef by stopping Mortimer's plans before accepting the White Glove Society portion of this quest may render it unable to be completed. Dialogue to Caesar will not include an option to indicate the White Glove Society will not revert to cannibalism, and speaking to Marjorie will direct you to speak to the dead or missing Mortimer.
PlayStation 3Xbox 360 After saving the Ted Gunderson and converting the White Gloves to cannibalism, the dialog options for Mortimer will close. However the quest will sometimes still direct the player to talk with Mortimer about converting the White Gloves to cannibalism. If they were converted to cannibalism, this glitch is irrelevant and the quest will complete (if the other conditions are still met).
Xbox 360 The Legion remained hostile even after receiving the 'Mark of Caesar.' Equipping NCR armor, exiting the Pip-Boy screen, then removing the armor within Perception range of hostile Legion members worked to correct this.