How to use cast-iron teacup?
I've never found cast-iron teacups to be practical to actually use.  Not only do you not want to warm them before pouring the tea in, after you pour it in the cups will be to hot to drink out of.  One has to wait for the tea to cool to lukewarm before it's safe to touch one's lips to the cup.

As far as cleaning them goes, you can use soap and hand-wash, just don't put them in the dishwasher.