Check out the soda threads regarding various forms of ginger beer, including by yeast and by gingerbeer plant (a sort of symbiotic yeast/bacteria thing like kefir grains).
You get carbonation by introducing CO2 to the liquid in a pressured environment. This is done either by force carbonating using a co2 tank, or natural carbing by letting yeast/gingerbeer plant eat sugar in a sealed environment.
If you want it as carbonated as sparking wine, or champagne style wine, you need a rather high amount of carbonation. More than you would beer. (meaning you need to make sure you have a vessel that can handle the carbonation level, like a champagne bottle.)
The rest is pretty loaded. There are studies and no one can still say exactly how champagne bubbles are formed. There are people who say that the carbonation styles are different, and that force carbing leaves a coarser bubble, whereas natural carbing gives a finer bubble.
Also, reducing the amount of ...things, yeast, protein, etc, in the liquid means that the bubbles will form slower.
There's so much, I think you'd better specify your question.