Install the override to allow House to gain control of the dam in the control room.
On the same floor, go southeast past the 2nd Tower exit (with the kitchen) and open the door to Hoover Dam Power Plant 1. It opens to a balcony with the switch that powers the East Power Plant on the western wall.
Go back topside to deal with the Legion and NCR on the eastern side of the dam.
Enter the Legate's camp to deal with Lanius. It is also possible to talk them into leaving the dam, with a Speech challenge (100 Speech) or a Barter challenge (100 Barter).
The Courier will spawn at Hoover Dam where immediately NCR Rangers will be fighting the Great Khans (if the Courier did not make them join them in the quest "Oh My Papa") and Caesar's Legion. The tower they must enter will be the third one on their right. They will see two NCR heavy troopers who will turn hostile if the Courier plants the override, but they can lie to them with a Speech check of 75, allowing them to use the override without having any of the NCR soldiers turning hostile, which is easier for their escape. Once the Courier has uploaded the override, they should head left until they find the door to the main power plant, where just outside there will be an electrical switch to turn on the power for the Securitron Army. The Courier should then head back in, find the key to the exit door and go back to the dam where only Legion and Securitrons remain, and head east towards Legate's camp. Securitrons will be helping the Courier fight their way to the camp.
Once at the Legate's Camp, they must either kill the Legate and all enemies from Caesar's Legion or convince the Legate to retreat with a Speech of 100 ("This battle is decided, that's why I am here.") or a Barter of 100 ("You could take the West. *Holding* it is another matter."). Instead of having to use Speech to fight him alone, you now just say: "Worth the gamble - now for the hard way."
Once they are done with Legate's Camp, they must head back towards the gate where they must deal with General Lee Oliver and the NCR army. They can either kill Oliver and his men or convince him to surrender the dam with a Speech of 100 (House's forces are much stronger than the NCR forces), Science of 100 (House can run the dam better than NCR), or a Barter of 100 (House agrees to protect Caravan routes). After dealing with Oliver, Mr. House will roll up in a Securitron Mk I, tell them Oliver and Kimball's likely fates, and end the quest and game.