Teresa,
I just scrape off as much of the spill as I can then let the
remainder cook on in the oven. It can be scraped off later when it is
cool. Stains are a way of life for a baking stone and do not effect
the function. Toppings usually sear quickly on the stone and then the
remaining liquid cooks out and the stone is OK.
As far as the smoking stone just leave it in the oven at full heat
for a while (an hour or so) and it will burn off any residual oils.
Unglazed tile, like natural stone and manufactured baking stones
contain water which turns to steam when heated. It is best to temper
the stone by heating to 200 F. for one hour and then increase it in
steps of 100 F every hour until the maximum temperature of the oven is reached.
I have used a Fibrament (bakingstone.com) stone since the mid 90's
and just replaced it. I had to cut the original stone down to fit the
new oven but it still worked well. I have never had the need to clean
it other than scraping off any spill residual. I use rice flour as a
release agent on my peel so I use "Dust Off" to blow the residual off
of the stone between loaves. It is easier and faster than brushing.
Good Luck
Pop