Can you recomend the best way using train, to get from Guangzhou to Wutaishan?

There is no direct bullet train between Guangzhou and Taiyuan or between Guangzhou and Xian.

You may take an ordinary train to Taiyuan from Guangzhou Railway Station. The train departs at 19:37, and the trip takes about 35 hours. Upon arrival, take a taxi to East Bus Station for CNY 10-15. Then, take a bus to the mountain. The buses are available from 6:40 to 18:30, and the trip takes 5.5 to 6.5 hours.

Actually, you are advised to fly to Taiyuan from Guangzhou (about 3 hours). Upon arrival, take a taxi to East Bus Station for CNY 35-40. Afterwards, take a bus to the mountain.:)

thank you very much Angela.i really appreciate your kindness and good advise.kindly
terry