It restocks 1 item at a time randomly throughout the day. You have to be pretty lucky to catch something there, but usually people will try to check once or twice every hour. Eventually you'll probably see a few things at least.
You use Wizard Tokens to buy the items there. The prices can vary depending on the item.
You don't really need to have any out in your inventory, it will just take them from your currency bank. I usually like to have at least a couple thousand in there for BHH or the Token Shop, it builds up quickly doing wizard quests every day.