China: Applied for a job at a big name local company via the internet. Got paperwork and Z visa (if anyone's thinking about China, this is a must, as working illegally is taken much more seriously than in the past). The company provided dormitory style accommodation.

If you're thinking of China today (that was 10 years ago) and do technology, the easiest way would be to get a job with a well known Western company such as HP, IBM, etc big names as a regular Engineer or QA perhaps at a junior lead level (assuming not going in as more senior management, which in any case is usually internally picked). I'm absolutely sure anyone competent in a similar role with 3+ years' experience can get in AS LONG AS you can convince you'll be comfortable in a completely new culture and stay modest, and I've seen it done with experience that's not that relevant, simply because diversity and English skills are very much in need and appreciated most of the time (a minority of managers can get defensive). Chinese language not needed in most international companies.