Sure thing. I don't have exact measurements, but I'll do my best.
>1. Fill a pot with 32oz of water. Use anything that is not tap water. Bottled, filtered, spring, ect.
>2. Finely grate about 2" of ginger (no skin).
>3. Add ginger into water and bring to a simmer
>4. Once the water is simmering, add 1/2 cup white sugar and mix to dissolve.
>5. Simmer the ginger/sugar water for 5-10 minutes
>4. Remove the pot from the stove and squeeze in the juice of half a lemon.
>5. Wait until the temperature of the water has come down to 80 degrees, freedomheit
>6. Strain the water into a 32oz bottle, or two 16oz bottles. You want your bottle to be pretty full.
>7. Add 1/4 tsp of dry active yeast to the entire mixture. So if you're using two bottles, that's 1/8 tsp each
>8. Cap it and shake it up
>9. Store the bottle somewhere dark and warm. The temperature should be around 70-80. If it's colder, it won't hurt anything, but the fermentation process will take longer
>10. Give your bottle a squeeze once or twice a day. Don't uncap it. Just feel the bottle to see how much carbonation has been produced. This is pretty variable. It could take 1-3 days before you notice any change. Also, your bottle will likely get cloudy on bottom and have some gunk around the top
>11. Once the bottle is nice and tight, you can strain/decant it into a final bottle. You will want to store this in the fridge to slow the fermentation process, but be sure to relieve the pressure at least weekly or your bottle could pop.
It will take some trial and error to get the ginger/lemon ratio where you like it. I use dry active yeast because I always have it lying around. You could use other kinds of yeast and see how they work.