Saga Airport is small but has daily flights to Tokyo (Haneda) and Osaka (Itami). Starting from July 2012 it also has flights to Shanghai (Pudong) every Monday, Wednesday, and Saturday. From the city it takes about 30mins by bus and costs 600 Yen.
Buses also connect Fukuoka Airport to Saga (70 minutes, ¥1000). This option to travel via Fukuoka is much more practical unless you need to use Saga Airport (flying in directly from Shanghai is going to be cheaper, but also less comfortable, than via Fukuoka due to the low-cost nature of the operating carrier).
Saga is a stop on the JR Nagasaki Line.
Limited express train services run from Hakata station in Fukuoka twice each hour (usually :02 and :22 past the hour), including the Kamome and Midori train services. Trains run directly to Saga in about 40 minutes at a cost of ¥2300. It is best to get the Return Ticket, as it costs the same amount but you save yourself the trouble of having to purchase another ticket to get back to Fukuoka. Even if it is unused, it doesn't hurt to get it as it doesn't cost you any extra.
Local trains from Hakata cost only ¥1080, but you will have to change trains in Tosu and the travel time will be about 75 minutes or more, depending on the timing of the connection.
From Nagasaki to Saga it takes 75-90 minutes on the limited express (¥3740), or about 2 1/2 hours on the local service (¥2070). From Sasebo it is about 65 minutes by limited express (¥2470) or about 100 minutes by local (¥1250).
The ruins of Saga Castle are free to enter. (150 yen bus ride from Saga Station.) There is nothing left there, but various history museums were built on the grounds.
Shanghai is fairly cheap to get to if you can make it to one of the three weekly flights (and have the necessary paperwork).