Mix water, sugar, and freshly microplaned/pureed/grated ginger.
Bring to boil for 2 minutes.
Remove from heat and cover to cool.
Add lemon and lime juice. (Zest of lemon and lime if desired.)
Sanitize fermentation vessel, airlock, and funnel - glass growler + rubber stopper + airlock + funnel.
Once 'wort' has cooled, sanitize hands, pitch Pasteur Dry Champagne Yeast, and transfer sanitarily to the sanitized growler. (Leave at least a few inches of headspace in the growler.)
Cap with airlock and store in a warmish, dark place for 2 days.

After two days, you can enjoy immediately in Moscow Mules, Dark & Stromys, or straight up. (If capped and stored in a warmish place, you'll likely have a mess on your hands. Refrigeration will slow the process, but you'll want to watch the bottle and consume within a couple of weeks.)

If a sweeter end product is desired with carbonation, dump growler contents into a pot and add simple syrup to desired sweetness. Bring the ginger beer to ~160F to kill the yeast, dump contents into a sanitized corny, force carbonate to desired CO2 level, transfer to sanitized bottles, cap immediately, and refrigerate. (Or enjoy straight off the tap. *buy more vodka)