I would like to visit China on my own. How do I go about it?

You should apply for a visa for that. You can apply for a Chinese tourist L type if you go there for sightseeing purpose. You should first prepare a filled-out application form affixed with 1 passport-style photo, your passport and its photocopy, your introduction letter, round trip air tickets and hotel reservation and an invitation letter from China, bank statement. Next, go to the embassy of China to submit the application.