While there is a similar instructable on how to make your own root beer, there isn't one for ginger ale. I've made my own ginger ale for years, and here's how.
Step 1: Ingredients/tools
--1c sugar (or less)
--small piece of ginger root
--a grater (microplane or fine holes) or food processor/chopper
--an empty 2L plastic (important) bottle
--around 2L of fresh water
Step 2: Ginger Root Preparation
Peel and finely grate a small piece of ginger. How much is up to you; it depends on how strong you want the final ginger ale to be. Try for 1T or so in the beginning, and if you want it stronger, add another half tablespoon; weaker, add less. I didn't measure the amount I used here but I like it spicy, and it came out fairly strong.
Step 3: Squeeze Lemon
I generally add a full lemon's worth of juice to this. If, like me, you don't have a juicer, roll the lemon between your hand and a hard surface a few times; this will help you get the juice out more quickly once it's cut.
Step 4: Put Ingredients in Bottle
To the empty 2L bottle, add:
--1c sugar (Again, taste comes into play. I like it less sweet, so I add ~ 3/4c. You may wish to add more or less depending on your personal taste. Add a full cup the first time you make it, and go from there).
--1/4 tsp yeast
If you're having difficulty with the sugar and juice, make a funnel out of a paper plate to pour everything in. Once everything's together, shake it around a little to distribute things.
If you're really paranoid about germs, you could prepare a weak bleach solution and rinse everything with it, but I don't see the point since you'll likely drink this before anything goes wrong. Just be sure to wash your hands before you touch stuff and you'll be fine (nothing adds tang like Clostridium!).
Step 5: Biological Carbonation
Fill your 2L bottle to an inch or two below the top with fresh water. Screw the cap on tightly, and shake until everything is dispersed. Be certain to flush the sugar from the nooks at the bottom of the bottle. The picture below shows everything in the bottle before it's been shaken.
Once you're finished, place the bottle in a warm-ish place (I set mine on top of the fridge, towards the back) and let it steep. Check on it every few hours by squeezing the bottle. When you can no longer push in on the bottle (i.e., it's become pressurized), take the bottle and put it in the fridge. This will slow down the fermentation and keep things from exploding. It never takes more than a day or so for me, but depending on how you vary the ingredients, things make take a little longer.
Note: I am quite serious about the exploding bit. If you leave the bottle just sitting in a warm place for a few days, it will likely explode and send sugary water all over the room. So keep an eye on it!
Step 6: Enjoy!
This stuff is best really cold. As with any yeast-based product, this will yield a tiny amount of alcohol in the final product. Really, I think it's less than a percent. You could easily drink the entire bottle and not have any issues. Those with allergies to alcohol, however, may want to be careful.
IanM23 made it!