I assume however it's done, it's a problem that has been dealt with a long time ago.

Theoretically, you're right - but every building is unique, and, unlike other fields of engineering, there are no breadboards, no prototypes, no boilerplate (except on actual boilers), no beta testing...

The greatest demand for water in any modern building, by the way, isn't the plumbing - it's the fire protection system. Here's an example (and pardon me if you know a lot of this, Tom - I'm "posting past you" to anyone else curious):

The amount of water required to serve any one floor is calculated from the number of sprinklers expected to be operating simultaneously in case of a fire, which is based on decades of actual fire experience (in parallel with continuous, scientifically rigorous testing) concerning the way the floor is cut up into rooms, the fire-resistance rating of the walls and the rooms' contents, and the hydraulic characteristics of the sprinklers themselves, of which there are many alternatives.

Those sprinkler characteristics - specifically, the volume/pressure relationship of water through an orifice of a given size - set the minimum pressure needed to deliver water to the single sprinkler farthest from the source (a.k.a. "residual pressure"). The pressure requirement for the remainder of the system on that floor is dependent on the physical arrangement and size of the interconnecting piping, all of which presents obstruction to the flow, mostly by way of friction.

The next major issue is: how high is it? As a rule of thumb, one pound per square inch of pressure will raise a column of water two feet (the actual relationship is: 0.43 psi/foot).

One more thing to consider - something called a "standpipe". You see them in stairwells: a vertical pipe with a fire-hose connection at every floor, or at every intermediate landing between floors. The NFPA code mandates both a minimum volume of water and the pressure at which it must be delivered at the highest point (which in turn is based on the standard characteristics of 100' of 4" fire hose, with fog nozzle). A single-standpipe system must have 500 gallons per minute available at a 'residual' pressure of 100 psi; the maximum requirement for a multiple-standpipe system is 2500 gpm at 100 psi residual.

Commonly, the standpipe load is the greater requirement by far; the code allows for combined standpipe/sprinkler systems whereby the greater demand suffices for both. So.... let's say, in this 1776-foot monstrosity, the highest occupied floor is a mere 1500 feet above the elevation of the underground water main. If you choose to serve the entire building from a central source, your task now is to arrange and size a pumping and piping system that will deliver 2500 gallons per minute at a minimum pressure of 850 psi (1500/2 + 100, at the pump discharge), to which pressure losses (due to friction) in the main distribution system and the standpipes themselves must be added - and remember to take into account the bursting pressure of various kinds of pipe materials as compared to the operating pressure of the system.... etc., etc..

Please refer to Nick's post for system alternatives - the same principles apply to "fire water" as to drinking water. You may decide that banks of "relay" pumps every few floors will be easier - recall, however, that you increase the chance for mechanical failure with every equipment item you add. Back-up redundancy in critical systems is a much a tenet of occupant safety in buildings as it is in spacecraft. Consulting various manufacturers' fire pump characteristics will eventually nail down required horsepower, which then gets passed on to the electrical group for sizing wires, breakers, and the back-up power system. Count on them telling you, "It's too much!".

Meanwhile: you're juggling all this in the arena of the project budget; loosing valuable design time by having to attend interminable - and, as the article implied, rancorous - meetings; fighting all the other trades for space on the floor and in the utility passages, horizontal and vertical... and must have it all approved by the City of New York and the insurance underwriter (probably Factory Mutual, whose criteria are stricter than NFPA's) before it goes out to bid...

... and that's just the FP system!