When selling a put option when is the contract fulfilled? Is it at any time between now and the expiration date, or is it only on the expiration date?
When you sell a put option, you are giving the buyer of that option the right to buy the underlying stock at the specified price at any day until the expiration of that option contract, in exchange for money - the money that they paid you for the option contract.
The buyer has the option to exercise that right, but he or she does not have to exercise that right.
Typically stock options are American style which means that the holder of the option can choose to exercise that right any day up to and including the expiration date of the option.
Exercise basically means that the holder of the option has to notify his broker by a certain time each day (usually about half an hour after the close of the main trading session). Then overnight, the seller gets assigned, and the stock is transferred from the buyer's account to the seller's account, and the money is transferred from the seller's account to the buyer's account.
In the United States, the Options Clearing Corporation has a rule where, on expiration day if the price of the stock closes at $0.01 or more in-the-money (the price of the stock is above the strike price of the call, or below the strike price of the put) the option will be automatically exercised unless the holder of the option provides contrary exercise advice.
For example, if I sell 1 put option for Dec 15 (12 days from now) at $40, and the current trading value is $35, is that contract going to get fulfilled as soon as the market opens in the morning?
Only if the buyer exercises the option. Often it is prudent for the buyer of the option to wait until the ex-dividend date (so he can collect the dividend) or expiration (there is no option premium left). It might be easier for him to make money by selling the option to someone else on the market.
Note: options exercises are usually allocated randomly or on a pro-rata basis - so it doesn't matter what the buyer of your specific option does, but rather how the clearer and your broker allocate assignments in a particular option among their customers.