I am doing the quest "underground undercover" and my quest log says "Talk to Desdemona" but I cant figure out how to get out of the institute so I can talk to her and proceed. How do I do it?

Teleport out, open up the map while on the outside part of the Institute instead of any department, click on the RR icon and teleport there.

You still don't get it, do you? You don't get out of the Institute... The Institute gets out of you!

You're this old and still believe in the Institute? The Institute doesn't exist, that's why nobody can see them. Everytime you hear about someone being kidnapped, it's just one of your parents dress as the Institute. They just want to scare kids into behaving.

I tried fast travel from various areas (including the area where you first come in and the central atrium) and all it says is "you cant fast travel from this location". Did I do something wrong?

I don't know what went wrong but I usually can teleport while not inside any building, go to the intersection where all the departmentd converged, that's where you usually teleport in and out.

Have you finished Institutionalized? I don't think you can get out before completing the quests Institutionalized or starting the quest Banished from the Institute.

Did you do the quest where Father asks you to meet some of the institute staff? Specifically after speaking to Madison Li she programs your pip boy to be able to fast travel in and out of the institute. She's usually in the Advanced Systems section. If you've been banished from the institute however, you need to take the central elevator back to the molecular relay you arrived at and then activate it's emergency protocols to get out of the institute.