As Shoshana said, call ext 8844 from your room phone. They will tell you the current offer. Having the reservation number for your current stay is helpful. They always ask for that, if I don't have it handy, they have used my phone number to find it. That proves to them you are a current resort guest. You can book any resort that is available for your dates. The reservation follows the usual Disney rules for cancellations & changes: 5 days cancellation for a room reservation; full payment at 30 days for a package. The deposit is due when you call, there is no courtesy hold on a bounceback. So have a credit card handy. No cancellation penalty as long as you are within the usual cancellation dates. So better to book if you think you might go back than regret that you didn't! You can always book then cancel if your plans change.
Changing depends on what is available when you call. You can't automatically add or drop days. But if what you want is available, you can change. Once the offer is expired, the regular CRO CMs usually can't make changes. They need to work thru guest services or transfer you there. No fee for changes, just any increase due to resort or room type.
How long it takes is just like any call to Disney. Sometimes quicker than others. You have the usual waiting for a CM, then verifying your info, checking for resorts, dates & room types & the booking process. The CMs have always been very helpful in checking availability. I have never felt rushed to decide quickly. But definitely don't call 5 minutes before you are leaving for a park or to check out. We go back to the room for an afternoon rest & that's when I'll call.
The last several years Disney has offered the room discount for the same year until early-mid August. Then they have changed to the
free dining offer for dates the following year. Some time in October, they have switched to a room discount for the following year. So if they follow their past pattern, your offer should be free dining for select periods in 2018.
You may find info in the Be Our Guest Guide if there is one in your room. Some people have gotten an email with the offer. Years ago it was on the TV. Even if there is nothing in your room, call & ask. You are eligible wether or not you receive information. If there is anything printed in your room, keep it. There is a direct number to the future stay department on it that helps if you need to call later.