How to travel from shenzen airport to Xiamen? I mean the best solution by bus or train? Pls. advice

There is no direct bus or train from Shenzhen airport to Xiamen. I suggest you take the airport shuttle bus from Shenzhen airport to Shenzhen Railway Station and take train to Guangzhou first, then take train from Guangzhou to Xiamen. Well, it may takes a long time. The best way is of course by air.