When is a customer's card charged?

At what point in the order process does the customer's credit card get charged?

I'm wondering what happens if a customer submits an order - it's in a "bid" state, then modifications are made, which adjust the price, before the order is confirmed.

Customers cannot pay for bids for this reason - it's still just a bid and changes may be made. As soon as it's moved to Order status, they can pay for it. However, most of the time you are protected from this kind of issue because once the order is moved to "Verified" status (meaning someone on your team has looked over the order and it's ready to be started), they can no longer make changes to the order.