I know about picking them for food. But is there a trick to make them show up in first place? Mine are very few and far between.

nope totaly random
but once you have more than one kid if your fast you can get two of them to pick the same mushroom

some things i have found is honering the temple,idol & dead w/alot of people gives you 2-3 mushrooms. an easy way to hunt them is hold a child & scan the board, when you find one drop the child on it and grab another child, in the later part of the game the mushrooms disapear quickly.