For our 2016 trip, we started planning/saving in 2015. We had tried a few times before to get savings going, but we just weren't in a place financially where we could even pay all our bills/responsibilities, let alone try to save for ANYTHING.
'Saving' for our 2016 trip was basically us setting the budget, and then saying, OK the package has to be paid off a month before the trip, we have X amount of checks between now and then, so let's break our budget up into chunks. I'd basically buy about $150-300 in gift cards a month at Sam's Club, bring them home, and add them to our Disney Savings account (online thing not offered anymore). Once we could book our package, we had a tidy sum in there. So then I would keep buying gift cards and bank them up to $500 and then make a payment on our package again. Rinse and repeat until paid off. We took nothing but Disney gift cards. Budgeted a small amount for the beach, but otherwise we were on site the whole time.
This time we are doing a mix of 'putting it on a card and paying it down ahead of time,' buying gift cards for things in the park I cannot get a discount on with my Disney Visa, and saving up cash to pay off the balance we use from my Disney Visa while on the trip.