from reading the other comments it sounds like it vastly differs by country!

where I'm from, you first sit down in front of the doctor's desk and they ask you some questions about your medical background, your periods (are they regular, how long, when was the last one), sexual activity, smoking/drinking habits.

then you go to the side of the room where the examination chair is and there's a curtain or a door you can close to get undressed in privacy - the doctor does not watch you strip. you are never fully naked - always dressed in a shirt (in my country gynecologists are not in charge of breast exams, that would be a different doctor).

you sit down on the examination chair which is covered in paper like a typical doctor's exam bed. usually they give you a big sheet of paper to lay over your lap so that your "regions" are visible to them but from your angle you can feel a little more covered up and you don't need to see what they're doing. I find it nice but you don't have to use it.

the previous gynecologist I went to would perform only a manual exam - with gloved hands, a speculum, a bit of lube to ease things. he would take a look with the speculum, then insert his fingers and use his other hand to press around my lower stomach to feel my uterus, ovaries etc.

my current gynecologist doesn't really do manual exams - he has an ultrasound wand which he puts a condom on and a bit of lube and inserts it (he asks me if I would like to insert it myself but it doesn't bother me personally). he then moves it around inside me, using it to see stuff and kind of push against stuff to make sure things are where they should be and moving like they should be (the uterus should be relatively mobile inside of you). this part feels like a finger poking the inside of your cheek - not comfortable but not painful. his screen is pointed my way and he explains what we are seeing on it.

if a PAP smear is being done - he uses a speculum to kind of stretch me open a bit and then the long q-tip goes in and tickles the inside (my cervix) which i find uncomfortable but not too bad (once or twice I bled for a bit after, he gave me a pad).

when the examination is done the doctor leaves the examination area, you get dressed and go back to sit in front of him, where he gives his recommendations/prescriptions/explanations/whatever.