Could someone teach me how to irrigate and underground farm? The several times I've tried have resulted in the deaths of many people.
The simplest way is
not to irrigate at all; just build farm plots on the soil layers. Of course this restricts you to the soil layers.
If you want to irrigate, the easiest way is the bucket brigade. First, make a well (or a bunch of wells, or designate a water source over a brook, etc.). Also make some buckets. You'll want at least 4 spare buckets at all times.
Figure out where you want the farms to be. Each farm plot will be 2xN tiles (anything from 2x1 to 2x10) with space between them. Figure out how big that area has to be, then dig it out. Then dig out a matching area
above that.
In the upper area, poke holes (channel) over each of the spots you want to be a farm plot. With 2x2 plots it might look something like this:
#########
#.......#
#.HH.HH.# H = channel
#.HH.HH.#
#.......#
####.####
Now, one plot at a time, designate
each channeled tile as a separate 1x1 pond zone. When a dwarf has "filled" a pond once (creating 1/7 water and mud on the tile below), remove that particular pond zone. The result will be a 2x2 muddy area on the level below, on which you can immediately build a farm plot. Repeat this for each plot.
For more details, see
How to farm.