Mushrooms grow on mycelium in normal light conditions.  If you plant them on grass or dirt they will pop up out of the ground when the light level exceed 11.

You can get mushrooms by putting a barrel full of water near to a mycelium surface. The conversion from water to witch water grows mushrooms on the mycelium. The witch water itself DOES NOT grow mushrooms, only the conversion process.

Mushrooms will grow into huge mushrooms when Bone Meal is used on them.

Nether Glowshrooms from the Natura mod will initially come from sieving Soul_sand  They will also become huge mushrooms when bonemeal is used on them.

But remember to keep your Mycelium away from your other grass or dirt, as it will spread.