If you want to book a Room Only reservation at a Disney resort with the CAA discount, you can book directly with Disney. But be aware that there are only a limited number of rooms per resort that are eligible for that discount. Once those are booked, you can't get that discount at that particular resort. You would have to show them your CAA card at checkin to prove your membership.
In order to book a vacation package, you would have to go through your CAA travel office.
I would take a close look at your travel dates to see if Disney doesn't already have a special offer that you could take advantage of. They are usually a much better deal than the CAA discount. Last fall I made a RO reservation and the CAA discount was 15%. I later changed that to 30% off with a PIN that I got.