After finishing Tranquility Lane your father will ask you to go with him back to Rivet City. You can say no and just meet him there later, doesn't matter which you choose. Once you do go back to the Science Lab there you will have a short conversation and then be asked to meet the scientists back at Project Purity. Head to the Jefferson Memorial to meet them.
Once there, your father will ask you to perform a few simple maintenance tasks to get the facility running. Just as you finish the last one, the Enclave shows up to take over the operations. (Spoiler) Your father then sacrifices himself so you can the other scientists can escape. Leave the Rotunda via the left door and find a sewer grate just to the left of that. Keep moving through the tunnels until you eventually come out the other side to the Brotherhood of Steel Citadel. Once Dr. Li gets you access to the city the quest will end.
See The Waters of Life for more specific info.