Peel and grate the ginger; you should end up with about 2 tbsp worth
Bring water to a boil in a small saucepan and remove from heat. Add the sugar and salt and stir to dissolve. Add ginger and let stand until cool, then stir in lemon juice.
Pour the ginger water into a clear 2 liter pop bottle with a funnel and top off the bottle with water, leaving a little over an inch of headspace. Give it a taste and just sugar and lemon juice as you like.
Add the yeast to the bottle, screw on the cap and give it a shake to dissolve the yeast. Then, be patient and let it sit in a warm place out of direct sunlight until it's well-carbonated. You can check the bottle for carbonation by giving it a gentle squeeze; when it feels solid, it's fizzy! (The carbonation can take anywhere from 12 hours to two days... just be patient.)
Refrigerate once it's carbonated; it'll last up to two weeks in the fridge but we're sure you'll drink it before then. BE CAREFUL when opening it for the first time... unscrew it slowly over a sink to avoid bubble-ups.
When serving pour it through a small fine-mesh strainer to catch the ginger bits.
Enjoy!