Process/type of visa for 3 month stay in china then backpacking

Hi, What is the process to follow and what type do I need to apply for? I will be travelling to PRC from the UK to attend a martial arts training academy for 3 months and then will be travelling on to Australia. I reside in the UK.
I have received a letter of invitation from the training academy, but not sure what to do next and the timescales involved.
Help would be much appreciated.