Make no mistake. Comstock House is no pretty mansion, it's a madhouse. The place actually starts out quite peaceful, that is until Booker steps into Her Loving Embrace. The key is to jog (not sprint) to where you want to go when the Sentinel looks away. If you are spotted, the seemingly harmless patients in the area will turn hostile and attack. In this case, it's best to just bash them to death with the Sky Hook, as there's no point in wasting ammo on targets that give nothing back. Equip the Vampire's Embrace gear so that you gain health for every melee kill. It keeps Booker healthy.
Press the intercom button across from the elevator thwn step on the lift when it arrives. There's a Voxophone in the elevator as well. A Sentinel is waiting at the Atrium as soon as you step out of the elevator. It's up to you whether to fight or sneak through.
Either way, don't forget to use the kinetescope next to one of the pillars here. Visit the Crematorium next (labeled "where we weep") and look into the wooden coffin for a Voxophone.
Climb up the stairs that was guarded by a pair of gun turrets then head to the end of the hallway (labeled "where we work") to find another kinetoscope. Just past the room with all the busts is another Sentinel. Grab a Gear and Voxophone at the back of the wall behind it.
Moving forward to the Security Center, look behind you as soon as you arrive for one more kinetoscope. Before going to the upstairs, check the room to the left where the lockers and weapons are. The next Voxophone is on a chair by the working projector in this area. Grab the Gear on the desk directly across from the stairs leading to the second floor.
Continue to the Warden's and pick up the Voxophone from the chair before opening the security gate. Fight your back to the elevator where you can score another Voxophone on the floor. You will eventually have control of Booker in the Operating Theater again after the somewhat disturbing story sequence. Now, you must fight your way over to the two generators for Elizabeth's torture chamber.
Free Elizabeth. Higher Learning achievement / trophy unlocked. After Booker regroups with Elizabeth, go back to that door that previously said "Elizabeth Busy. Can't Lockpick." and open it.
Inside the doctor's office is the last (24th) Infusion phial and the 76th Voxophone. If you've been following this guide up until this point, you should now have all the Infusion upgrades which unlocks the Infused with Greatness achievement. Follow the objective arrow to the elevator.