I don't know if this is any improvement on the wiki but:
think of a pump as having four squares:
OXX+
O: this is the square water is drawn from. it should be an open space with some source of fluid in the level below.
X: the first part of the actual pump. must be built on a floor, can be stood on by a dwarf. when you build it, the building placement should actually be an X of approximately this color
X: the second part of the actual pump. can be built on a floor or overhanging an open space. serves as a wall to creatures and fluids
+: where water is pumped to. must be a floor (or a fortification), and will cause fluid to flow into any neighboring square not blocked by door, wall, etc.
the goal is to pile these up in a 'pump stack' so that each pump is drawing fluid from the square that the pump one level below it is pumping to. in other words, looking from the side you will see:
OXX+________
+XXO
OXX+
+XXO
OXX+
=
so get a power source, such as windmills or waterwheels. use gear assemblies and axles (also in 'b'->'M') to bring power to wherever you want you pumps to be. then for as many levels as necessary built something like
888888
8.+.+8
88+888
88X+88
888888
(where "." is an open space, "8" is solid rock, and "+" is a floor and "X" is a staircase for access)
on one level, followed by its reverse on the one below it,
888888
8+.+.8
888+88
88X+88
888888
it should end so that the open space furthest from the center has water or magma immediately below it. you can skip the open space in the middle only if you're willing to either use dwarf-power to pump or if you're willing to go to the trouble of running mechanics and axles to ever pump; otherwise you need them to keep your pumps connected in terms of mechanical power.