How you do determine how many elevators are needed in a skyscraper? Is there a rule that you use?

Dont think there are rules. Extensive studies have to be made into the logistics of a skyscraper, not just the elevators, but also the number of floors each elevator connects, the number and size of normal doors, emergency stairways, hallway-width etc.... Safety would probably be the key in the design. During an emergency, it should take, say 10 minutes to evacuate the whole building.

Not a simple matter of dividing the number of people using a building by a given constant.

The size/capacity of the elevators is also taken into account. Some buildings might require only one or two elevators but with a huge capacity, while other building might be better suited for four elevators but with a small capacity.

These days many new skyscrapers create new ways of giving space for the lift shatfs. Norman Foster has designed Sydney's 126 Phillip Street with a core -free floor. The 9 lifts are located in a 150m high atrium which is attached by bridges to column free office space.
Lift cores take up way to much room. this is a novel idea indeed.
http://www.126phillipstreet.com.au/images/features/TypicalFloor-May022.gif