What's the best way to find a job as an expat in Beijing?

Browse the employment classifieds on http://thebeijinger.com. Mostly teaching jobs but there are some real jobs there as well. http://Linkedin.com and http://Glassdoor.com also have some decent job listings, and if you read Chinese then also try http://zhaopin.com and http://jobs.51.com, although most of those will be aimed at Chinese workers so the employers may not be able to sponsor your visa - there are some English postings on those sites as well though.

Teaching English is definitely the easiest way, especially for private English-learning institutions, such as EF (http://www.ef.com.cn/englishfirst/default.aspx) and Wall Street English (http://www.wsi.com.cn/cn/index.html), etc. It only requires you to be easy going. Most of the classes focus on listening and speaking, so as long as you are a native English speaker, I don't think any kind of "English teaching certificate" (if there is such a thing) would be required. No Chinese language capacity required. I do know a couple of people who see such teaching jobs as their "step-stone" to a "real job".

Depends on your field.english teacher is a easiest way.or other foreign enterprises...

Network, network and network or how chinese call it: 关系 GuanXi. I've personally known many people not very qualified for a job get it just because they were recommended by a friend. AND they get paid hefty sums of money -,- Another way (much harder) is to look through job postings. Some sites include http://51job.com, http://yingjiesheng.com (mostly for fresh graduates) and even http://linkedin.com. If you have Wechat, you can even follow the company there. Some companies often post job vacancies through it. If looking for English teaching jobs, then your best shot is sites like http://thebeijinger.com or http://echinacities.com. Good luck! Job hunting can be pretty frustrating, especially in China.