As elsewhere in China, there is an extensive rail network; Guangzhou is one of the major hubs. Rail is the main means of inter-city travel for the Chinese themselves, and many visitors travel that way as well. The system now includes fast bullet trains on some routes; unless your budget is very tight, these are the best way to go — fast, clean and comfortable.
All the major cities have airports with good domestic connections; some have international connections as well. See the individual city articles for details.
There is also an extensive highway network, much of it very good. Busses go almost anywhere, somewhat cheaper than the trains. See the China article for more. Driving yourself is also possible, but often problematic; see Driving in China.