Go into the guest booking and look for the words "Change or Cancel" and you'll see a screen with all the details. If the guest wants to extend the stay (or shorten the stay), simply put in the new date. In this case you'll put in the new CHECK OUT date, and then go to the TOTAL $ and change the price to reflect the new total. The total $ does not always automatically update so make sure that you double check this box carefully.
I use the "change or cancel" function all the time to alter the booking. I use it if someone asks me to extend the stay, I also use it to charge extra in situations where there are extra guests for some of the days but not for all of the days, and I've also used this process to charge for broken wineglasses. As long as the guest stay is active, ie not yet checked out, you can alter the booking. Once you alter the booking, a "request for approval" is sent to the guest and they must ok the change. Then you are sent a new confirmation email.
I used this just yesterday, as I welcomed a group and they showed up with two extra guests. I think they were thinking that they would be sneaky (I charge an extra guest fee). I didn't even blink an eye, I just said Hi Alexis, welcome. I see you have two extra guests, no problem I will just submit a booking alteration to correct the guest count right now and you can approve it asap, then I stood there and waited for him to approve the change to the total, and only then did I leave.