In your Ready Room, connected to your bridge (not your quarters) on the wall opposite your desk (always been the same for me) you walk over there, and similar to how you access your bank or other ingame things (a little pop up for you to click or hit F) and you should get that pop up, then its pretty straightforward from there... This is Federation ships.
In KDF ships its in the Mess Hall which is on the Crew Decks, I believe.
Also you can't place all ships on there, only particular ones, which sucks, its really horrible the limited amount of customization for your quarters/mess hall/ready room.
Cloaking generators break down at first sign of language.
You can also avail of the trophy shelves in the Federation interior mess hall too. The mess also allows you to place ground trophies, which can be obtained from various missions as well as coming 1st in various fleet actions.
The shelves also support non-ship trophies rewarded from accolades (like plaques and cool themed stuff) - again if you have earned any.