How do I get from Guangzhou Airport to the train station to buy a ticket to Changzhou, JiangSu?

You can take the Airport Express Line 1 to reach the CAAC Ticket Office (near to Guangzhou Railway Station) and then you can walk to the railway station to buy a ticket.
Actually, you do not need to buy the ticket at the airport. I once used the https://www.travelchinaguide.com/china-trains/ to search the train schedules and book the tickets. It is very conveninet and they can deliver the ticket for you.