Getting around in Hubei is fairly easy. Buses go to most cities or at least through them, just let the driver know where to stop. The same goes for getting on the bus, just put out your thumb and a bus will stop for you and tell you how much it costs to go where you want to go.
Hubei also has a decent train network, like the rest of China, however it won't go to quite so many places as the buses and often it is very busy.
Within Wuhan and many other cities in Hubei, bus is the best way to travel. The average fare is ¥1 for non-air conditioned/heated and ¥2 for air-conditioner/heater. Given the amount of people on buses and the fact that someone will always have a window open, often it is best just to save the extra ¥1 and go the cheap option.
Taxis are also relatively unexpensive. Flagfall is ¥6 for the first 1.5km