Hi, you couldn't purchase a ticket at Beijing Airport. And, it is also difficult to get one on the same day at the railway station. The train ticket from Beijing to Guangzhou is needed urgently. The fastes train from Beijing to Guangzhou will take 20.5 hours and costs about 450RMB/hard-spleer/one-trip. So, if you will not travel in the peak season, please consider flying to Guangzhou from Beijing directly. The airfare is almost the same with the train fare.

There is no train ticket office at the airport, you may buy it at the train station or some payboxes scattered in the city. And, there is no round trip train tickets, just one way ticket. For detailed information of price and travel time, which is very informative.
Besides, the train tickets are always under great demand, you could buy it 10 days in advance.
Good Luck.