You simply take your pass to any major park Guest Relations window or to either of the two DD Guest Relations offices. Tell them you want to upgrade the leftover days to a "______ pass" (fill in the blank with the pass you want).
They will issue you a credit based on what you originally paid for the pass and how many major park days remain unused. Unused plus options carry no value for upgrades. Example: You paid $100 for a five day pass when you bought it and you have one day left on it, you would get a $20 credit towards the new one.
It's never really cheaper to upgrade old passes since you will usually have paid less for the old one per day at the older price than you will for the new one at today's prices.
My advice would be just use the old day and buy what you need from that point on.