To climb the stairs to the very top, one must purchase tickets and take part in a guided tour. The tour starts on ground level where the guide (a young bella Italian woman) tells you many facts about the church. After a bit, you begin the first climb, up the first 150 steps until you reache the first tier terraces (which I didn’t know existed). Here you see beautiful views looking South. There is room enough for several hundred people onthis wide terrace, unlike the top of the dome; which is some 300 more steps. The guide leads you to front of the church and you can look down to the Baptistery, then walk along a very narrow ledge (luckily, it has the 4 foot stone rail-wall) and go through a low door, drop down a few steps into the inner walkway, just below the Dome Fresco. I've added a picture here so you can get an idea.
You then walk about 50 feet, then back up and out on to another small ledge and find yourself on the other side of the lower terrace looking off North.
This terraces leads to the entrance to the final steps leading up to the very top of the Duomo. It is a difficult climb – very steep and steeper even more. The passage way is room enough for a small man, so when meeting someone coming down the exact same way, one has to back up or squeeze by if the size permits. It is very tight.
You can spend as much time as you like at the top.
Here is one picture of one of the views