The nearest airport is Jerez de la Frontera (35 Km) where several airlines fly from Madrid and other European cities.
(Kindly check with your travel agency for further details).

There are buses from the airport to Cadiz as well as a taxi service available (55 euros).

The airport of Seville offers more domestic and international connections but is located 120 Km away.

There are also trains connecting Cadiz with different cities (again,check with your travel agency for details).