Vodka is an pretty easy spirit to make, as it requires no aging or maturation. While vodka can be made from most grains, arguably the best source for the alcohol is the humble potato. You simply ferment it and then distill it. Distillation is the trickiest part, but with a short trip to your local sciences shop, you can pick up the parts to build a stove-top still and start making homemade vodka in your own kitchen.
Wash and peel your potatoes, and then chop them up into cubes. About 1 lb. of potatoes is enough to make about 1 pt. of vodka.
Put the potatoes into a pressure cooker. Fill the pressure cooker with enough water to cover the potatoes, plus about an inch or two more. Then clamp the lid on and cook until the potatoes have fallen apart and dissolved into a mash. This should take about an hour.
Pour the potato mash into a plastic vat and let it cool to room temperature. There is no need for a thermometer. Just put your hand over the mash and if it doesn't feel warm, it's cool enough. Pour in some yeast and start fermenting the potato mash; 1/3 tbsp. will do, and the best yeast you can find commercially is probably going to be distiller's or wine-making yeast. Let your potato mash ferment in the open for one to two weeks, depending on the local climate. When the bubbling starts to slow down and become less frequent, you will know that fermentation is concluding.
Fill a heat-safe beaker sufficient to hold at least 6 qts. with fermented potato mash, and put a rubber stopper with a hole for both piping and a thermometer into the top. If you cannot find rubber stoppers with the requisite holes, cut them yourself with a pocket knife. Put that beaker on a stove burner.
Put a coil of copper or glass tubing into the stopper. Install the condensing jacket around the tubing, and fill it with ice water.
Put a second rubber stopper with a hole for tubing into another beaker and then put the other end of the tubing into that stopper. This second beaker needs to be big enough to hold at least 1 pt. Set this on the countertop.
Light the burner, and heat your potato mash to a point between 173 and 200 degrees. This causes the alcohol in the mash to vaporize, but not the water. The alcohol vapor will then rise into the cooling coil, condense and drop down into the second beaker.
Clean your cooking beaker and distill the results a second time. Most vodka you buy on the shelf is 40 percent alcohol, and it is unlikely you will achieve that concentration in only one distillation using stove-top methods.