I have serious grounding issues; my guitar buzzes very much, but if I touch any metal parts it's decreasing. I have some pictures of wiring if you want. I want to know how to locate broken or loose ground wire.
A few things I can tell you, the first and most obvious is the cable. If you can decrease the hum/buzz by touching ANY metal parts and/or strings, then your guitar ground wiring is probably "OK", meaning it is probably as good as the manufacturer took the time to make it. But a crappy cable will always make things a lot worse, especially in an electrically noisy environment, and especially if you use high gain effects pedals (such as compression or distortion). Don't forget... there are speaker cables that have the same 1/4" phone plug on each end, and aren't shielded at all. Try your setup with a good quality guitar cable first.
Next, an amplifier that has a switch that offers grounding options can help a lot! Some even have a 3 way switch, which connects audio ground to either AC supply wire (though a capacitor for safety), or "lifted" (meaning no ground at all). This is both to offer options for minimizing noise issues with improperly wired stage outlets, and to offer an option if your microphone shocks you when your hands are on the guitar. If your amplifier has no such ground switch, you can at least verify that the ground pin on the AC plug is connected to your chassis ground, and that you're not plugged in to an older 2 conductor outlet through a ground defeat adapter. You'll also need to verify your AC outlet is PROPERLY wired. With a multimeter set to "AC", you should be able to read near full house voltage (120VAC nominally in the US) between the ground pin hole and the SMALLER rectangular power hole (to the right of ground is ground faces DOWN), and you should measure near zero ( or just a few volts ) between ground and the larger rectangular hole. And by the way, if your house /socket wiring is part of the problem be warned: You may run into this again at a performance, and you'll need to be prepared!
Finally, it doesn't hurt to look around inside your guitar and see what grounding optimizations can be made. In addition to checking continuity between ground and the string holder as another poster suggested, check whether the metal cases of all potentiometers and switches are soldered to ground, and that ALL interconnecting wire between the pickups, switches, pots and output jack, are done with braided coaxial wire. If they aren't, then short of re-wiring your whole guitar there's little you can do other than avoiding this manufacturer in the future. Good lick!
The basic grounding wire for the strings may be with the string holder accessible when unscrewing the back panel from the guitar. That's where mine sits.