The closest airport from Yangshuo is the Liangjiang International Airport (两江国际机场), this is the only airport we have in Guilin and Yangshuo, 1 hour by car from Guilin, 1.5 hour by car from Yangshuo.
To the airport, buy the tickets at ticket office at Yangshuo bus station or Sam can help you schedule a private ride at anytime, even last minute.
From the airport, you can just buy the tickets at the arrival hall. Public transfer can be a bit messy, and if you have a lot of luggage or travelling with many people or need more comfortable ride, Sam can help you book private car transfer, better deals than the taxi guys at the airport. Rates depend on the size of the vehicles.