I think it works something like this: When you swallow your food or fluids, they normally travel past your tongue, into your throat, down your esophagus, and into your stomach. A small area where your esophagus meets your stomach normally maintains a relatively high pressure so that your stomach juices don't come up into your esophagus and give you heartburn and other troubles. When the pressure in your stomach overcomes the pressure in that area, the lower esophageal sphincter (LES), you burp. (It looks like the LES also relaxes on its own sometimes, so it's not necessarily excess gas that causes people to burp.)
I suppose it's possible that you just have a 'strong' LES that maintains an abnormally high pressure. The reverse happens, people have a weak LES, causing heartburn, hiatal hernia, and gastroesophageal reflux disease. If that were it, I'd bet that you don't get heartburn often either.
Anywho, taking a swig of water, tilting my head all the way back, and then swallowing allowed me to swallow enough air to get a decent vibration. Drinking with a straw is supposed to help also.
If you really want to know how to belch like a pro, you can look up something called esophageal voice (a.k.a. esophageal voicing, speech, or phonation). Normal voicing results from a vibration of the vocal folds, but when they aren't working for whatever reason, people can use another type of vibration: belching. I just stumbled upon this, so I don't know much about how it works, but it sounds cool -- they speak by belching.
I wonder what technique Dan Castellaneta uses for Barney (on the Simpsons).
(Oh, and hehe, I said sphincter. Twice!)