Turn it on
Campaign → Settings → Physical prize shipping. Do this before you draw, so the winner emails carry the address link.
What the winner sees
After the draw, an address form appears on the campaign page. The winner email links straight to it. Only actual winners can submit — the form checks the entry against the results before saving anything.
Addresses are stored separately from entrant records and are never collected on entry, only after someone has won.
Fulfilment
Dashboard → your campaign → Shipping lists every address, split into to-send and sent. You can record a tracking URL and a note per item, and 'Copy all' gives you the whole list as plain text for a courier form or a spreadsheet.