For your first farm, don't bother with any fancy irrigation...
Irrigation is a bonus and will make things grow faster, but a layer of soil provides a quick way to get things moving without much work (or risk of floods).
In theory, yes, but in practice a non-irrigated TC farm is almost useless. VERY slow, very sparse.
Irrigated is the way to go, and "learning by
doing making mistakes" is the dwarven way.
So, here's a relatively safe and simple irrigation plan:
Dig a tunnel from
next to your river (don't breach!) to roughly the
middle of your future TC farm, and up to it. 2 tiles wide should be ample, ramps or stairs should work fine.
Now, the trick is to use a pump on the surface level to provide the water and the pressure. Build your pump next to the river - (if it's a brook you'll have to channel 1 tile of the brook for the inflow - don't breach the tunnel!). For the outflow, build a retaining wall around the start of your irrigation tunnel.
It will look like this:
xX( ) __________(surface)___________
~~~ |_|= ____TC_ _Farm____
River |_|===================|_|
xX = pump
( ) = small walled retaining area on surface, to contain outflow of pump.
|__| = channels, ramps, and/or stairs up to next level
So, this is a passive system - a connection directly to the river is
never channeled out, so it won't do anything unless manned by a dwarf, and it doesn't need any levers or floodgates. Start the pump pumping, a dwarf will respond, the retaining wall will try to fill but will drain down, the tunnel will fill, and the water will start welling up out of the far end.
When at least 1/7 depth has covered
almost the entire area (yes, you have to keep half an eye on it, so
you are the point of failure!), go to the pump and tell it to stop pumping - order it deconstructed and then cancel that, and/or <A>ctivating the dwarf will do fine and be immediate, no lag.
The water settles out, evaporation begins, you can then seal up the tunnel or ignore it as you choose (even if you later, accidentally, breach the river/brook, the u-bend won't cause flooding if it's on the same level.)
(A linked drawbridge in middle of the tunnel will allow you to seal it for certain maintenance changes, and is good safe practice in a non-critical situation.)