My first ever journey to Moiyan was aboard the T8370 train from Shenzhen. The journey took around 5 hours. I paid 73RMB for a 'soft seat' but should have paid a bit more in order to get a sleeper - much more comfortable!
Note that the rail station name is MEIZHOU 梅州.
I used he China Train Guide website to check train times from the UK. Although not an official website, it was surprisingly accurate. The main problem with buying train tickets is that they are generally only available to buy 10 days before departure. You will also need to know how to ask for the ticket in Chinese.