Traditional ginger beer is fermented, and the fermentation process takes sugar. Sugar free ginger beer is also alcohol free, and it has a different taste than the traditional drink. It is a drink you can share with your kids, and is a good alternative to other kinds of soda. It is also a good thing to drink when you have the flu, since the soda bubbles and ginger root are very soothing for the stomach.
Grate or dice about two tablespoons of ginger as finely as possible. Put it in a small jar.
Squeeze a lemon into the bottom of the jar. Leave it soaking for about an hour to let the ginger soak in to the lemon juice.
Strain the lemon juice through filter paper into a large mason jar. Add seltzer water to fill it up.
Add the sweetener of your choice. Xylitol and aspartame both taste pretty good with ginger beer. Stevia also works and is a good all-natural alternative. Some people like a very sweet ginger beer, while others prefer less sweetness.
Pour and drink up. Screw the cap on when you're done to keep the ginger beer from going flat.
You can also use a soda bottle. If you do, you will have to use a funnel to pour the lemon juice in.