With the latest patch, the game introduced mushrooms to grow them underground. This special plant can only grow underground and on mud plots.
How do you generate those mud plots?
Mud plots are generated by flooding a room that is adjacent to water as shown in the screenshot below. There is also no sunlight to be allowed to shine on the mushrooms.
At the moment there is no other way to generate those plots for the mushrooms.
If you have a specific place you want a mushroom farm, you could also strip the floor above on a 2x2 box and wait for it to fill with water - extend that out to 3x3 and so on, extending only one axis (3x4, 3x5, etc). Once your area is sufficiently large enough, drop a floor on it (all but 3 spaces so the water is replenished) and tunnel underneath for your farm. Repeat as required:).
You can also make a rain pool, it looks ugly but it works.
Designate it as an underground farm you will have a 8 tile farm. The rain will flow down the ramp to the farm, you could make it from the 3x3 step on level 0 but rain is randomly generated and it could happen that no rain will fall into your rain pool.
I noticed by excavating that with an enough deep ramp you can create a new pool of water, so I tried it with mushrooms both work.
As @Noneofyourbusiness had stated it is a matter of putting water and letting it dry up to become mud.
The way I did it was one level below the water supply. I created a large enough plot of empty land which should hopefully absorb and distribute the water.
On the level with the water bottom of the water supply I create a 3X3 area with a hole in the middle. When all is ready I just cut the hole to the water supply and funnel it down to the bottom level.
This will totally empty the lake rendering it practically useless since after 11 years rain won't even come close to filling it up. The only thing useful thing that it can be converted to may be a lava moat, though I haven't gone that far yet.