FYI, I usually work with some variant of the following side-plan...
fakeedit: slightly ninjaed by slothen, whose briefer picture is probably more specific to your situation... diagonals, or timely operation of floodgates, is very important in order to avoid flooding when sourcing water from higher levels than you're tapping it off, though... Do watch out for that. If in doubt, put doors on the entryway(s) to the "well room" so that you can limit flooding to there until you've undone any initial problems you inadvertently encounter...
Water comes from any source you want/can get...
(I usually tap into Cavern pools from the side, once I've found a suitable spot to do so with)
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v
#####
#W_<_ <- Underground dwarf access to well
# #X# <- stairway down to 'reservoir' level
??≈F≈≈># <- water level, with a floodgate (for creature access control)
########
To dig any height of well, I tend to stack channel-designations, vertically (without any side connection), meaning that a digger will channel the spot he or she stands on (except maybe for the top layer, before there's a first channel to go into to reach the second) and fall (generally harmlessly) 1Z down in each attempt, until reaching the intended bottom of the well (or the last level before breaking through into caverns, if going in from the top, which needs to be dug from a side-access, to be safe, and then a hatch put in to close off in case of flyers, before sealing this last side tunnel as well)... then they either dig their own escape-tunnel to the side and up, or make use of one that another digger has been making simultaneously.
An alternate method is to make a stairwell immediately adjacent to the intended well-shaft, and then set the well-shaft channels to be dug from safety of standing on the stairwell. Either way, I tend to plonk a hatch on top of the stairwell, just in case I need to discourage any of my dwarves to wander down the stairs, or block anything nasty that's in the well (perhaps with the fortification-flow bug) from getting out that way... You could floor over it, but you might anticipate someone being shoved down the well by a tantrumming fellow, and want to give them an immediate chance to get out (assuming they can swim).
An alternate-alternate method is to make the well-shaft a stairwell-shaft at first but then (after ensuring there's another exit, perhaps from the side and ready to be walled up again, or perhaps a secondary escape-stairwell), progressively (i.e. sequentially) channel away the stairs from the top on down to 'open it up', enough to let any bucket pass down. But I consider that method messy, so rarely use that.
Top-plan view of water-tapping operation (on Z-level of the water I want to tap)
Water
≈≈≈≈#######
≈≈≈≈####### <- find a handy 'step' in the water's edge
≈≈≈########
≈≈≈########
≈≈≈########
Rock (undug)
≈≈≈≈#######
≈≈≈≈#######
≈≈≈##,#,#,# zig-zag path dug, almost to a diagonal 'step' in water's edge
≈≈≈#,,,#,#, (red bit of rock is next in line, but would breach water)
≈≈≈######## Green bit of rough floor is also dug out, to allow next step.
≈≈≈########
≈≈≈≈#######
≈≈≈≈#######
≈≈≈##,#,#,#
≈≈≈#XO,#,#, Put a floodgate in on the last bit of tunnel
≈≈≈######## Attach to a lever and pull to open
≈≈≈######## Put a temporary wall (green) in to restore the zig-zag
(wall can be placed as soon as dwarf has attached first mechanism to floodgate,
even before second mechanism is attached to the assigned lever.)
Smooth (at least) the red "breakthrough" tile (although I tend to smooth everything that will be my aquacourse's walls/floor)
≈≈≈≈#######
≈≈≈≈╔══════
≈≈≈╔╝+#+#+#
≈≈≈║XO+#+#+
≈≈≈╚═╩═════
≈≈≈########
≈≈≈≈#######
≈≈≈≈╔══════
≈≈≈╬╝+#+#+# Set the red 'breakthroug' tile to be carved to fortification
≈≈≈║XO+#+#+ (the floodgate tile will be 'open', of course, but I've left the 'X' here anyway
≈≈≈╚═╩═════
≈≈≈########
While the engraving dwarf is making the fortification, set the floodgate lever to be pulled again...
It will not close while the dwarf is in the way, but (as long as not delayed), as soon as the fortification is made and the dwarf wanders away from the wall it'll close, meaning only a little water will leak through
≈≈≈≈#######
≈≈≈≈╔══════
≈≈≈╬╝5#1#+# (showing not atypical water-levels for the zig-zag, temporarily,
≈≈≈║XO3#+#+ as if you have "display as numbers" on to show 7ths of fullness...)
≈≈≈╚═╩═════
≈≈≈########
≈≈≈≈#######
≈≈≈≈╔══════
≈≈≈╬╝1+1+1+ Dig further walls (and temporary one)
≈≈≈║X+1+1++ and optional smooth...
≈≈≈╚═══════
≈≈≈########
≈≈≈≈#######
≈≈≈≈╔══════
≈≈≈╬╝776777 Dig further walls (and temporary one)
≈≈≈║X777767 then when everyone's clear, open the floodgate again...
≈≈≈╚═══════ I like to get it filled to 7/7ths globally, then shut the floodgate, but that might not
≈≈≈######## be possible, and might not be necessary...
(You can re-open the floodgate if the water level lowers, when you're sure there's nothing (contaminants/hostiles)
that can somehow get through the fortification and make the water dangerous, one way or another.)
Anyway, no matter what the water-source, you now have successfully tapped it. Variations on a theme can have further exits from your initial reservoir (pre-prepared with closed floodgates) leading to secondary/tertiary reservoirs on lower levels, or pumps drawing it upwards above the original water-level (where possible).
I also use a similar sort of method for tapping magma. Generally my "floodgate closes as soon as the fortification is carved" method (ensuring magma-safe materials are used for the floodgate/mechanism!) means that the carver immediately vacates the area where the (slower to flow) magma would be pouring in, and thus escapes general
‼death‼ or any related injury. But with water the danger is drowning, which the zig-zag (need not be as long as above) is intended to mitigate, the carver easily outrunning the initial water which is 'de-pressurised' at each diagonal. The magmaducts I make are generally for the benefit of magmaworkshops, and thus once I attain a 7/7ths fullness of the magmaduct I can (as of the current version, although who knows if it'll change in the future) close and
keep closed the floodgate, to maintain a constant pool of uncooling magma that is free of magmabeasts wandering through it, regardless of what happens in the adjoining magmasource. (Which I
might even try draining...)