Have a quick glance at the whole song, and aim at a verse at a time. If your wife will let you do the washing up (mine is generous in that respect) sing it to yourself till you know it- when you've got one verse, start on the next.
If you are really ambitious, you can try TWO verses in one washup. Mind you, you may have to wait for a day when there's a burnt porridge pot AND a scrambled eggs pot to deal with.
After a few days, you should be well on the way to the last day- putting it all together- good luck