Here is what you do...
On your first park day, get there a little early, and find the Will Call window. It is one of the ticket booths, except at MK (where there are no ticket booths), where it is usually the Guest Relations windows outside the turnstiles on the right, or on rare occasions the small round building nearby. There will be a sign with an arrow pointing which way.
Tell them you are redeeming your Give A Day Voucher for the free ticket, and give them the voucher (not required, but makes it easier) and your ID (required). ASK them if you can upgrade it to a 2-day (or whatever) ticket. They will likely say you need to use it first - if so, no big deal. Some CMs will apparently upgrade it right then and there. If so, you pay the exact difference between a 1-day MYW base ticket and the target ticket, including tax.
If they don't upgrade then, you can do so at any time at your convenience before you need the additional day(s) (and within the 14-day upgrade limit) at ANY ticket booth or guest relations location.
The difference between an adult 1-day base and 2-day base is currently $80+tax (savings of $2+tax).