One thing that I wish I had done when I started brewing Root Beer was to test it out first. It's a moot point now, I would be here regardless if I had started out with a test run first or if I had bought all the brewing equipment up front (which I did). But, what if I didn't like the taste of brewed Root Beer? What if I had wasted $100+ to sit in my closet with a wife to nag about everytime she had to see it? This is why I believe that this test run is to important to your brewing success. It's a lot easier to say "I don't like this" when you only spent $5 on everything rather than buying a bucket, bottles, siphon, filler tube, caps, sanitizer, etc.
Here is an easy extract brew that takes no more equipment than what you probably already have in your house and a short trip to your local grocery store for the things that you don't.
Equipment and Supplies:
1 Empty Two Liter Soda Bottle w/ Cap
Measuring Spoons and Cups-1/4 Teaspoon, 1 Tablespoon, and 1 and 1/2 Cup
Funnel
Sugar (1 and 1/2 cups)
Yeast (1/4 Teaspoon)
Root Beer Extract (1 Tablespoon)
Lukewarm (100-105*) Tap Water (Enough to fill the 2 liter bottle)
The Basics:1) Make sure that the Soda Bottle is clean. Did I mention that the soda bottle should be CLEAN?

2) Put the sugar and yeast into the Soda Bottle. You can mix it up if you want to but this is not necessary right now.
3) Pour in the extract into the Soda Bottle. Try to get as much into the sugar as possible for it to dissolve easier - but don't worry if you missed.

4) Put in enough Tap Water to fill the soda bottle about half full. Make sure that the water is the right temperature - too hot and you may kill the yeast, too cold and it may not re-activate from its dormant state.

5) Put the cap on the bottle and shake the heck out of it, we want to tr
y to dissolve as much of the sugar and extract as possible.
6) Fill up the rest of the bottle, leaving about 1 inch headspace.
7) Recap and shake the heck out of it again.
8) Put the Soda Bottle in a warm dark place and check everyday. The bottle will get harder to squeeze every single day due to the build up of Carbon Dioxide.

9) Once the bottles are very hard to squeeze -at least as hard as a soda pop from the store (usually 2-3 days depending on the temperature) put the bottle in the fridge to chill for a day or two. It is important to put the Root Beer in the fridge at this point-chilling the brew slows down the yeast activity whereas if you left it out it would continue to build pressure until it blows.
10) Enjoy your home brewed Root Beer!
Some Things to be Aware of:-This will not taste like store bought, soda pop Root Beer! It has a slight yeast taste to it. This taste can be changed depending on the yeast that you use but will not go away.
-There will be a small yeast deposit at the bottom of the bottle. Some people don't like the taste of the sediment so pour carefully to avoid it if you wish.
-The taste clarifies and more yeast settles the longer it has to sit in the fridge.
-To add more mouthfeel to the brew add a teaspoon of Maltodextrin. A word of caution you will have to shake the dickens out of the bottle to get the Malto to dissolve (boiling it in water and then adding it to the bottle works the best-just make sure the water is the right temperature when you add it to the bottle).
-You can tweak the sugar levels and extract levels to taste-just make sure you add enough sugar to carbonate.
-You cannot naturally carbonate with artificial sweeteners.
So, you just brewed your own Root Beer. Doing it this way taught a few lessons; 1) Brewing Root Beer really isn't that difficult-you can make it as involved as you want it to be, 2) It does take time-you're looking at 4-6 days before you can enjoy your brew, and 3) Brewing is a fun hobby!