Wood ear is きくらげ, sold dried in small bags and, more and more, fresh. It is the same mushroom you find in Chinese, Vietnamese, Thai and Korean cooking, so it is one of the easiest Asian ingredients to get in Japan.
きくらげ
kikurage · dried, in small bags
生きくらげ
nama kikurage · fresh, in the mushroom case
白きくらげ
shiro kikurage · white (snow fungus), for sweet soups
In the shop
Dried: the dried goods shelf (乾物), next to shiitake, kombu and harusame noodles. Fresh: the mushroom case in the vegetable section.
Which shops
Dried in every supermarket. Fresh at larger supermarkets; often grown in Japan (国産). Gyomu Super sells big bags of dried, already cut.
Watch out
Dried wood ear grows about seven times its size. Soak 10 g in water for 20–30 minutes, cut off the hard base, then cook. Don't eat it raw.
Lazy Recipe sees that you're in Japan and turns any dish into 3 steps with what Japanese supermarkets sell. Your shopping list shows each item's Japanese label and aisle.