What is the best travel method from Guangzhou Airport south to Shajing Town?

For Shajing Town, do you refer to the one in Shenzhen?
If so, from the airport south subway station, you can walk to take the airport shuttle bus to reach its terminal at Civil Aviation Ticket Office. Then you can walk to reach Guangdong Provincal Bus Station to take the direct buses for Shajing Town. Upon reaching the town, you can take taxi to reach anywhere you want to go in the town.
The timetable for Shajing is 06:40, 09:00, 90:40, 10:40, 12:40, 13:00, 13:40, 15:40, 17:00, 18:20, 18:40 and21:00.

Thank you Jimmy!

If I understood you correctly...

From my airport arrival gate, I can walk to Gate A9 for the Civil Aviation ticket office and terminal.

Then I can walk to Guangdong Provincial Bus Station to take the direct buses for Shajing Town in Shenzhen.

The timetable for Shajing Town is 06:40, 09:00, 90:40, 10:40, 12:40, 13:00, 13:40, 15:40, 17:00, 18:20, 18:40 and 21:00.

Upon reaching Shajing Town, I can take a taxi to reach my final destination.

Am I missing anything? Thank you again!

Actually, you need to get shuttle bus line 6 to Tianhe Terminal, close to the local East Railway Station, near which you can easily find the East Bus Station where there are buses to Shajing. Upon arrival at the town, you can take a taxi to your destination then.
Well, buses at the East Bus Station for Shajing are scheduled from 06:55 to 19:45 every around half an hour.