I really ought to put together a "Big Book of Dwarvenly Projects" sometime...
Anyways, there's five ways to dam a river:
1) Wait until it freezes. Channel ice, put in whatever. Not applicable in your case, since your map doesn't freeze.
2) Pour magma on river. Channel obsidian, put in whatever. Not applicable in your case, since you don't have magma.
3) Collapse natural stone over river. Again not applicable.
4) Dig either a) a very large cistern, or b) an alternative river path underneath the river. Include some way to block off this alternate path. Once that is complete, dig out the floor underneath the river, so it falls into the cistern/alternate path. Put in whatever while river is diverted. When your dam is complete, block off the alternate path. Done.
Side view:
~~~~~~~~
XXXYXXXX
XXX XXXX
XXX XXXX
XXX X
XXX X
XXX X
XXXXXXXX
Where Y is where you'll breach the river's floor. Installation of floodgates or drawbridges hooked to a lever to block water flow is encouraged before breach. If you use a cistern, it must be *large*. It will fill very quickly.
5) Hook up screw pumps (approx. 1 per tile river is wide), pointed either back upriver or to the side, with some walls to keep the water from spilling downriver. Attach pumps to power source (not manual). While pumps are running, put in whatever.
Top down view
....~~~~....
....~~~~....
X...~~~~...X
X...%%%%...X
X...%%%%...X
XXXX~~~~XXXX
...XXXXXX...
This may result in construction getting suspended a few times; keep unsuspending it and it'll eventually finish. I did this in the "Founders" succession game in the Community forum, if you want to grab the save and take a look.