For the actual room's cost itself, you'll be charged after you checkout (using card). This does not include the deposit however, and it's likely you'll pay that upfront before you check in (for me it was $150 upfront cost @ Hilton). Last year there was a statement about possibly being charged for the room deposit before the convention begins, but that hasn't happened to me.
I always make people pay asap well before Fanime even begins. I do this because there is always that last minute "I don't have much money, can I pay you back when I get paid?" excuse and then you're out of that money for Fanime -- and of course the risk of not getting paid at all.