My husband and I are on a cruise stopping at Madeira in December. What would you recommend that we do and/or see in a day, please?

Stroll in the city center of Funchal, visiting the Cathedral (Sé)and watch the women selling flowers on the main street nearby. Go up to the Park of Santa Catarina, the view is gorgeous.
Walk down to the market "Mercado dos Lavradores". Catch the cable car (teleférico and climb up to Monte, where one of the atractions is the Monte Palace Tropical Garden and Church Of ur Lady of Monte. Go down the hill back to Funchal by the famous "carros de cesto", wickerwork sledges pushed by two "carreiros", the sledge drivers, slide on wooden runners for 4 km down to Funchal. It´s fast and it´s funny. It´s a not to miss when you are in Funchal.
One day is short.
An early arrival of your ship could perhaps give you time to take a cab to the Botanical Gardens, which is quite remarkable too. It could be your starting point. If not, you will already have had a good view of Funchal and surroudings for a day.
Enjoy it!

Hi, kind of depends exactly how much time you have and what time you arrive. If you have just a few hours the usual touristy thing to do is to get the cable car up to the top, look round the church etc. and maybe the botanical garden and then come most of the way back down on one of the old wooden tobogans. You can walk to the centre of Funchal from where you'll dock in a few minutes. There is also an open top bus tour of Funchal which would take a couple of hours.
If you really do have all day there are organised minibus tours or most taxis will do a full day tour for a fixed price. If you can't do the whole island we did a tour of the west side which was really good. Have a good time.
Hope this helps.
Regards
Tricky Dicky