You cannot get to Santo Antão by plane. There used to be an airport near Ponto do Sol, but now it's abandoned.
There are 2 ferries per day between Porto Novo, Santo Antão and [wiki=111c7859cf317f55a94468a7c7cbd5c9]Mindelo[/wiki], [wiki=432d6a6bcefacae85aead196d0da86c9]São Vicente[/wiki], and these are run by two separate ferry companies. Both ferries accept foot passengers and cars[url=http://www.bela-vista.net/Ferry.aspx].]There are rumors of rough journeys across the channel in between the two islands, where vomiting passengers line the sides of the deck. However, with careful choice of a calm day, the journey is pleasant and offers some interesting views of both islands and the Ilhéu dos Pássaros (Bird Island) just off Mindelo. Also, passengers may be able to spot flying fish and dolphins out in the channel.
ARMAS (Boat: Mar d'Canal) run 2 journeys a day Monday to Saturday, departing Mindelo at 8.00 and 15.00 and departing Porto Novo at 10.00 and 17.00. On Sundays there is only 1 journey, leaving Mindelo at 8.00 and Porto Novo at 17.00. Departures are prompt (and sometimes early), so aim to be there ~30 minutes beforehand if travelling by foot. The journey takes ~60 mins and tickets are available in Mindelo at the Terminal de Passageiros (outside, left hand side of terminal) and in Porto Novo inside the Gare Maritima (ground floor). Tickets cost 800$ (~8€) per adult per journey. Car prices vary, but start at ~80€.
[url=http://cvfastferry.com/v1/]CVFastferry[/url[/url] (Boat: Liberdadi, a catamaran) operate 2 journeys a day on Mon, Wed, Thur, Sat and Sun leaving Porto Novo at 8.00 and 15.30 and Mindelo at 9.30 and 17.00. On Tuesday and Friday there is 1 journey only, leaving Porto Novo at 8.00 and Mindelo at 17.00. Tickets can be booked online, as well as in Mindelo in the blue historical building on Praça Dom Luis and in Porto Novo at the Gare Maritima.
It might be reasonable to rent a car in Porto Novo for 50 euro