Check out the requirements for entering Spanish territory at link, specially the list of countries whose citizens are required to obtain a visa.
The high-speed AVE trains whisk passengers from Madrid to the Gijón in approximately three hours, depending on the specific service and intermediate stops.
Timetables, prices and tickets at Renfe.
Asturias airport is the closest. It is located 40 km from Gijón. The airport offers a bus service through the company ALSA that covers the journey between the airport and the city of Gijón.