First, let's assume that you have another job as well – I only know one person who makes a living just from literary translation.
Starting out as a literary translator is a bit of a chicken-and-egg problem: no one will pay you to translate if you don’t have a track record, and you can’t get the track record until… etc.
One way is start small: find a short story or an essay you like, and contact the author for permission to translate it. Write/phone/email the publishers if you can’t get hold of the author’s details. The author can be well known or not, it doesn’t matter, but prepare something on his/her background for potential publishers.
Then translate it. Then offer it to literary magazines, or websites. Which ones will depend a bit where you are in the world. You could offer it to Paper Republic, for example: propose it for the Read Paper Republic project by emailing firstname.lastname@example.org. Or pitch it to Words Without Borders, Asymptote Journal or similar literary magazines. Mostly you won't get paid for this kind of thing, but it will be a useful exercise. It will prove to yourself and to potential publishing contacts that you can do it; also, you may get useful comments from fellow translators who read it.
Once you have something you want to translate, whether short or long, look out for translation awards and prizes for which you can apply. American PEN, for example, administers a rather prominent one. Winning an award will raise your profile and that of the work you are translating.
At the same time: Do some translation training, read books about translation theory, attend workshops – it helps you reflect on how you do your translation and why. Look out for translation summer schools, for instance, in the UK, the Warwick Translates Summer School or, in the US, Middlebury. These programmes change every year, so please let us know at email@example.com if new ones start up or old ones are no longer running.
Keep an eye on literary translation websites, and websites with a general Chinese-to-English translation element, for jobs, news, information and so on.
Join a translators’ association – either a specialist literary one or a general translators one. You will often have to do a test translation to be accepted as a member, but it will mean you can be listed in their directory.