One useful technique for establishing voice-one of the most important in the case of the written word-is increased use of particular words or phrases. For instance, a character might favor a particular curse word, or a particular silly euphemism for a curse word. Or, a character might extremely rarely say some words, or usually use short or long words (e.g., the Thing uses short words, Mr. Fantastic uses long words, or as the Thing would call them, five-dollar words). A character might also say "little old me" or something a lot.
Mentioning the Thing brings us to another facet of voice-dialects and accents. The first real master of accents in American literature was Mark Twain, and he established it as a literary tradition here for the most part.
Of course, writing good accents is tough-and thick ones are hard to follow. (Try reading molespeech from a Redwall book if you don't know what I mean, hai burr ai.) Numerous Brits and Aussies complain that Americans imitating their accents mangle them. And while you don't hear the complaint much, lots of fake Southern accents are really bad. (My theory is that Southerners are too polite to complain most of the time.) Of course, the real reason they complain is because the accents must be exaggerated in order for them to be obvious in fiction-it's just the nature of the beast, and it's generally easier to do something ridiculous with an accent than make it perfect, because a realistic one will be too subtle for many readers.
Then there's quirky speech patterns that can't really be attributed to an accent, or to normal but excessive use of particular words. There's not really a word for this, so I'll simply demonstrate:
Tell me where he is... or I'll nail you both to the ground, yes?
That, in case you don't know, is Death's Head. Most of his sentences, for no apparent reason, have a "yes?" or an "eh?" tacked on the end. There are other quirks, like the tendency to refer to oneself in the third person, which can also create voice.
Hmm... What next?
Ah, yes, there are also nonword vocalizations, such as "hmm..." which may be used more or less by certain characters.
Can these techniques be overused? You betcha. In many anime, especially those aimed at somewhat younger audiences, use of peculiar phrases becomes remarkably excessive (although these are, thankfully, usually removed when dubbing into other languages). I can't tell you how much hearing "na no ne?" at the end of every freaking sentence someone utters irritates me (although it hardly helps that the character in question has a really grating voice).
The one last part of voice, and one that is not always relevant, is the sound of the voice itself. In written works, the only way you can indicate a voice is with descriptions of it. Otherwise, people will just imagine it for themselves. In an audible medium, obviously the sound of the voice will take care of itself.
I hope I don't come up with another half-dozen things to add tomorrow. That'd be annoying.