Now that The Institute has made its presence known to the surface world (see Powering Up), there's no time like the present to do away with the opposition. Your first target: The Railroad. It's a brutal task, but nothing can be left to chance.
If you have an established allegiance with The Railroad, you can knock out this quest quickly, starting with a fast travel teleportation from The Institute to Railroad HQ. If you and The Railroad are mere acquaintances, you can reach them the same way you originally made contact with them: via the Old North Church catacombs. When you've made it inside, simply kill Desdemona to turn the entire faction against you.
All the key members of The Railroad should be at headquarters. The one exception might be Deacon, who has been known to wander. If that's the case, the waypoint indicator will reveal his location. After you've eliminated The Railroad, return to Father at The Institute for a conversation.