You don't season a baking stone -- the pores must be open to cook things
properly.

You dont clean a baking stone, other than to scrape off any obvious burned-on
black stuff. The heat of the oven does short-term cleaning under normal
conditions.

The stone will be cleaned ultimately during the oven's self-cleaning cycle --
after which you just wipe off any grey power with a damp sponge.

-- Larry