The two closest (about 100km) international airports to Ourense are: Santiago (SCQ) and Vigo (VGO).
Madrid airport (MAD) is another possibility because it is well communicated with Ourense by train.
There is a Bus route between the Airport and Santiago, stopping at different points in the city, including the railway and bus station. Taxi is another possibility.
Train Santiago-Ourense: It takes about 40 min. More information in renfe.com
In this case the best option is to take a taxi, the price is about 100 euros (one way) and it takes about 1 hour.
The Airport is connected by Metro with the railway “Chamartín” station, it takes about 45-50 min and the cost is 4.5-5 euros.
Train Madrid-Ourense: It takes about 5h. You can buy the ticket in renfe.com. The ticket price (one-way) ranges from 18 euros in tourist and 59 in business. It is possible to take a round ticket (72 euros). More information in renfe.com
The best option is to take a taxi to your hotel, about 5-7 euros.