what is the best way to coordinate flight from the U.S. (atlanta, Ga) to Jinan, China?

The bus from JN airport runs at 11:00, 13:30, 17:30 and 19:30.
For the lay-over time, to be honest, I am not very clear about what you mean, so would you mind confirm it for me again?
As I know, there is no direct flight from USA to JN, so you need have to transfer in Beijing or HK.
If you land in Beijing, the time for custom is around half an hour to one hour according to the numbers of the passengers.
The all kinds of weapons, weapons, simulation of weapons, ammunition and explosives, counterfeit money, audiovisual products (harmful to Chinese political, economic, culture and morality), poisons, psychotropic substances, drugs, noxious animals as well as plants, food and other things from epidemic area are not allowed to enter China.

Hi, my question is can you give me an approximated amount of time that I may be laid over between flights from Atlanta, Ga to Beijing, ? Also, is there a train that I can take from Jinan to Dongying City? if so, how much does it cost and how often do they run?

Which airline do you use?
As I know, if you use the flights of United Airlines, you have to transfer twice before reaching Beijing. For most cases, the fist transfer place is in Houston, TX, with only about one to two hours to transfer. Then you have to transfer in San Francisco, CA with a lay over around one day.
From JN to Dongying, there is only one train, 5011, running about 4 hours and 20 minutes.
The fare is 30RMB for hard seat and 47RMB for soft seat.