I started collecting kashigata - special carved wooden moulds for making wagashi (sweets). But strangely enough I'm having a hard time finding information on how to use them.
Often made of sakura (cherry wood) and seasoned for about 3 years before carving, kashigata were used to make dried confectionery made of rice flour and sugar called rakugan... Kashigata were also used in the making of wagashi (nama-gashi or freshly made cake and hi-gashi or dried confectionery) for tea ceremonies.
On the blog "My Wagashi Chronicles" the explanation of the technique is pretty straightforward:
This is usually shaped into ornate, thumbnail-sized shapes in wooden molds where they become dry and stiff before being tapped out and arranged in pretty boxed collections, most often to accompany the somewhat bitter matcha tea in a tea ceremony. But there are larger versions to give as gifts or display as Buddhist altar offerings on holidays like today
It sounds like they are basically just molds like any other, just made of wood. So "clean before using" them. If you are having trouble with the type of wagashi you are making you might check out that blog and email the author, or perhaps it might be the recipe for wagashi you are using (check out @Elendil 's first link; some are more sorted for molds than others). Once you try, if you identify any actual problems, try posting it.