Use the high speed trains to get around wherever possible, not flights
I found that most places I wanted to visit in China were on the high speed railway network
These trains are super nice and convenient, and flights in China are almost always delayed. And the train prices are anywhere from 1/2 to 1/3 cheaper than flights
Beijing to Shanghai, for example, is only 4 hours and 20 minutes by train if you take the fastest one (Fuxing line). And the normal class (2nd class) train ticket for this route is about USD$90. It's almost guaranteed to take longer than this on average by flight if you factor in the potential delays and how not easy it is to get to the airport
I usually use Ctrip to look up the schedule. This website is pretty modern and easy to use. But I never buy tickets online, because I found it to be a major hassle to get the tickets delivered to you if you don't have a permanent address in China. Just buy it from the train station with cash and passport
One thing I don't like about the train station though is lining up to buy ticket is stressful. People will cut in line all the time and it's really annoying