After talking to Elder Lyons, he is going to order the launch of Liberty Prime. Follow Sarah Lyons and meet up with the rest of the team outside the Citadel.
After meeting with the rest of the Brotherhood of Steel soldiers, follow Liberty Prime to the Jefferson Memorial.
After reaching the Jefferson Memorial, head inside to the Jefferson Rotunda.
You can choose to fight Colonel Autumn or tell him to give up and let him walk away.
After speaking with Doctor Li over the intercom, she is going to let you know that one of you has got to head inside and start the purifier before it's too late. To get a good ending, you will have to go inside and sacrifice yourself.
The code will be 2-1-6, reffering to Revelation 21:6. Once the code was entered, a final cutscene will play, showing a statue of Thomas Jefferson in a purified water. The character will pass out and die afterwards.
A series of images will show your actions throughout the game.
This was the Fallout 3 Walkthrought I made, I hope you found it helpful.