My usual method goes something like this:
Channel the hole in the floor where the well is going to go. Hope I get a miner who's eaten/drank recently.
Start channeling the area around the hole to desired depth, but leave the first ramp you created so your miners and whatnot can still get out. Mine out the drainage tunnel (if necessary, I've had a few mishaps). What's a drainage tunnel? Let's say you build your cistern like so when you're done:
_____o______
=== ===X
\__/
The left side is your mined 'pipe' bringing the water in (we'll get to that in a second). The right side is the outflow. You can drain off the edge of the map. What I'll typically do is run a pipe to the map edge, smooth that wall, then engrave a Fortification into it. That allows the water to leave the map with no risk of flooding the halls. I typically do this because my cistern is part of my waterfall system and the waterfall absolutely has to have an outflow, so I just build it entirely in one shot. The alternative is the diagonal water pressure removal that's listed above, but I find safe better than sorry. It also keeps water from getting stagnant.
So, back to the cistern. You've got your ramp in, you've dug a bit of hole around it deeper. Now, you need to drive the pipe over towards the river. That's a simple mining command, stop 3 squares short of the river. At the end, dig a stairway up, then U/D stairs till you're at the bed of the river. Dig 2 squares towards the river. There should be a single square of dirt between you and the floodwaters. Have your guys build a fortification in the last square, then install a floodgate in the second to last square (make sure the fortification finishes before the floodgate installs). Finally, install a lever somewhere ABOVE flood level (aka: ground level) and hook it up to the floodgate, just in case everything goes to hell in a handbasket. Channel out the square between the river and the fortification.
Your water system is good to go. Flip lever, see what happens.
If everything is going according to plan, flip the floodgate back into place, let it drain a bit, and then go remove the access ramps and create an access stairway with another floodgate out of the bottom. Retest. Should be good to go at that point.
Of course, if you want to be dwarfy about it, just set up a chain of screw pumps to the main stairway and use the bottom of it as your well.