Economics, politics, sport – there are more Chinese names popping up in your scripts than anytime (since, I guess, the 2008 Olympics. Sorry this guide is six years late).

Some of the bigs ones, most broadcasters are achieving ‘good enough’; for others, this guide will get you there, and you can be confident you’re doing yourself justice with a very important language group.

Xi Jinping: Xi, is his surname, and is in essence pronounced see, or sea, or the letter C. Some broadcasters will say something along the lines of Huhsheeee. This is unnecessary. It’s not wrong, but it’s not necessary (and reflects a specific historical track in teaching Chinese overseas, so just don’t bother).
Likewise the Xi of Bo Xilai.
Jin: like the Jing of Beijing, is a hard j. Js in Chinese are not Spanish or Scandinavian (jin ≠ yin), nor are they French – they are Just, not Juste. The capital of China (smog not withstanding) is not Beige-ing, it’s Bay-jing.
Bonus: I believe this holds true for Korean too, so Kim Jong-un is not Young’un.

Bo Xilai: Bo is not beau, it’s just boh, or an RP baw.

Ding Junhui: You’re all getting the surname right! Ding = sound of a bell. Jun, remember, the hard J. There really should be a bit of rounded lips on the u, but you’re doing fine without it.
The Hui though, you probably need to work on. ‘How did Ding Junhui play?’ rhymes (or is it scans?) – Hui rhymes with way, not we. Keep pronouncing the H, just merge it into the -ui. Hway. Without the H, it sounds like Wei, as in Ai WeiweiI/eye Way-way. Easy peasy.
Fengshui fits in here too – shui rhymes with way, just stick an sh ahead of it, while Feng is more like fung.

Those are easy enough to merge together, right? That comfort you have with merging sounds is useful in Mandarin pronunciation. So, now that you know how to pronounce Xi, you can say Xiang – siang. The i and a are not distinct individual letters – run them together.

The A, inside words, is one to note. It is often more like an e than an a, so xian is more like sien (the city Xi’an is different). The difference here is also to do with the nasal ng at the end. Xian – sien; Xiang – siang.

Wang is basically Wong. Sorry, lame punsters. To balance this out, where there is an O it is stretched, so Dong is not a merry door bell but a drawn out church bell, almost like the start of the French Anglais (with a D ahead of it, of course).

Back to merging sounds – the Diaoyu Islands are not Dee-yao-you. The d and iao really need to be run together, so it’s worth practising. If you can, say, differentiate between meow and meeeeow then you’re well underway on that. It applies with other [consonant]-iao or -ian words too, Jiao, etc

Zh_: A slightly thick J, is good enough. Zhou is more or less pronounced Joe. Zhong, more or less Jung. Zhang is like the woman’s name Jan with an ng instead of the n.

Z is different from Zh – but it is still pretty uncomplicated. A bit more buzzy than zit or zip or zing, but not need for lots of tongue rolling and whistling. Zi at the end of a word is not Zeee. Think more zih.

Xi’an: the apostrophe indicates two separate syllables, so pronounce each on it’s own, don’t run them together. It’s easy, you went to see Ann. The apostrophe also points to particular  word which has been mispronounced on-air for so long that it’s almost correct to use the incorrect pronunciation, as an anglicised form which the listener understands.
But should you wish to explain Tian’anmen Square to the editor, here goes:

Tian = Tien. Anmen = An mun/mehn. Meh with an n on the end. In Tian the vowels run together – Tien rather than ti-yan. Tien an mehn Square. The same applies to Tian Tian the panda in Edinburgh zoo. It’s tien tien, rather than tee-ann tee-ann (which as you can see is four words rather than two). Sorry, Eddie!

A couple more places: Hunan v Henan. Hunan could be Galafray Granny – Who-nan. Henan is far from He-Man, more like Huh-nan.

Another sportsman: Formula E driver Ma Qing Hua. Properly written Ma Qinghua, Ma is the surname, and ‘qi’ is very similar to ‘ch’,  just with the tongue forward in the mouth. So Qinghua pretty much equals ‘Ching-hwa’.
And updated for 2019: the Formula E host city Sanya is two  syllables, san and ya, and there is a little bit more stress on the ya (which rhymes with that dance, the cha-cha. Sanya is on the island province of Hainan, which is hello grandma, high-nan.

Aside from that, you are already getting Mandarin names right, or certainly into the ‘good enough’ territory for news bulletins and informed interviewers. Names from Hong Kong or overseas Chinese will usually follow different rules.

Note Chinese names are usually given in the form [Surname] [Given name] – so when the CNN ticker (long long ago) referred to the Chinese Premier Wen Jiabao as “Mr Jiabao”, they were wrong.

Who am I to tell you this? I have a degree in Chinese from SOAS, and my pronunciation is really good – on the phone I’ve been mistaken for a native speaker. I’ve worked in radio news and features, in the BBC Chinese Service and others.
There are other resources out there to help with this – across the BBC you can access the Pronunciation Unit by phone or email, and I believe they publish lists on the intranet. For the rest of us, there is still the guide provided by the Voice of America – – memorise that web address, whatever about this whole guide!