There are a few ways to find housing easily on the island. One option is to get in touch with previous or current students to find out where they stayed and check if it is available to rent. You can do this on the MHCI or MET Portugal facebook group here and here.
Then click on "Pesquisar" to issue the search
Students Accomodation from Madeira University
You can book accomodation here: http://www.sasuma.pt/portal/index.php?id=asolicitar