Ok, hospitals obviously vary in the way they do things but this is how my scope days go.
For morning scopes, admitted at 8.00am, you will be allocated a nurse and he/she will show you to your bed/cubicle where you will be asked to put on a gown.
Then he/she will come ask you about your medical history and any problems you have, he/she will tell you whats going to be happening and hopefully give you a rough time when you will be done, of course they can run late so don't hold them to it.
You will get a hospital id bracelet and told where the loos are and so on, then you can sit back and relax while you wait for your turn.
When your turn comes they will take you to the day theatre where you will lie on the bed, left side, Dr will put a canula in your hand to give you pain relief/sedation, you will have a BP cuff on and usually an oxygen nasal clip.
Then off you go, they will pump some air into you to get a better view which can be uncomfortable and you may be asked to change position now and again as it helps getting the scope round the bends. You should able to watch it all on the screen. If it gets too uncomfortable or painful, tell them and ask for more sedation, no point in trying to brave it out.
Once done, 30 mins max, you go to recovery where they monitor your BP for 15 mins or so then they will take you back to your bed/cubicle to sleep it off, maybe an hour, depends on how the sedation had affected you.
Then cup of tea and bics or sandwich, they need to see you eat and drink before they let you go. They will have phoned whoever is collecting you and once they arrive you should be able to go home, provided things went to plan out by late morning/lunch time. Of course that depends on the time you had the scope but they will have the afternoon lot due so won't keep you longer than nec and they plan to get everyone out by then.
You will need to rest for the remainder of the day and not drive or operate machinery for 24 hours.
Hope that helps, as you can probably tell I have had a few done and will have many more in the future!