Spoiler Alert
This guide has spoilers in it, read at your own risk.
How to get to the loot
First of all you will need lockpicks and blue frog sash (you can get the sash from killing some blue frogs or if you enter via tracking skill you will be located in the locker room where you can find it along with gas mask), do not enter without lockpick because you will not be able to craft them in, or got out and then in again.
Get to the Foyer, from there go either west or east, and then head north, you will get option for lockpick, and then in the room you will get another lockpick option “Check the safe” and that is how to get the juicy loot. You will get 3x Cure for blue rot, Revolver with 12bullets and Nanokit with 2 charges.
How to get out
From foyer head west and then “Go west through gated doors”, approach figure, tell her you are still new, ask her what she means to do, *optional* ask about the challenge, agree to help her, go to foyer, east wing, go east to the auditorium, keep listening, make your challenge, accuse the bishop, For now i always used skill Eagle Eye, but you can use Trapping or hiding as well (but i do not know the outcomes, if you do pick it feel free to leave the outcome in comment and i will add it under yours name.) so if you choose Eagle eye you get to know that the bishop is trying to trick you to think he wants other challenge then the trial of light, so you choose to refuse, that will result in trial of water.
(see outcomes of all 3 trials bellow), as you get to the end of trial you get to choose “reward”. And will get out of the institute.
The Three Trials
If you choose the Trial of Water, they will waterboard you. The water that enters your system will eventually induce gastroenteritis. – most recomended trial as it does not result immediate injury.
If you choose the Trial of Fire, you are put in an oven and nearly burned/asphyxiated to death before being pulled out.
If you choose the Trial of Light, you will be put into an electric chair. Surviving is only possible with the Tough skill, though with injuries.
This text was sourced by fandom wiki.
Suggestions
If you know anything that is not stated in this little guide feel free to leave a comment or add me, i will add to the guide creators and you can write it in under your name.
A lot is not included in this guide, for example how to get to the second floor, always i try to find out i get instantly killed by some monster. (this is explained by user GabrielFlood in comments)