What I would be using to distill my "mash" this afternoon if it were legal to do so is something called a disappearing or cone still. The cone still is an ancient invention that have been described in Egyptian tomb writings. The healing women of old made cone stills to distill water to make it safe to drink, essential oils to concentrate their healing herbs, and alcohol to make disinfectants and bases for their tinctures.
The term disappearing still comes from more modern day people who needed to be able to dismantle their still and make it disappear into the cupboards so the 'revenuers' wouldn't catch them. Most people have what it takes to make a cone still in their kitchen right now.
The first thing you'll need is a pot. The bigger the pot is the more mash you can distill. The pot should be made of heat resistant and non-reactive material. Stainless steel is what most people would have, though copper would be better. Copper reacts with the fusal oils that are in alcohol and make them less potent. Fusals are another thing that can lead to hangovers. Stainless steel works fine though. Again, you'll just get rid of the first 1/4 to 1/2 a cup of distilled spirits that comes off the still and you'll be fine.
The second thing you will need is something for a condenser. A stainless steel bowl or wok works the best. You can put a good amount of snow or ice into this and so you won't need to refill it as much. If you don't have something like this though, and the lid of your pot is concave, you can use this. You'll just have to replace the melting snow or ice faster.
The next think you'll need is a collector. Again it needs to be heat resistant and non-reactive. Also it needs to fit inside the pot with room to spare. This is a pyrex measuring cup, but a glass bowl or smaller stainless steel pot will do fine too.
Then you should raise your collector off the floor of your pot. This is a stainless steel steamer with the center post removed. Anything heat resistant and non-reactive will work though, even small, very clean rocks. If you can't find anything, it isn't totally needed but without it, you may lose a bit of your alcohol as it re-evaporates from being heated up sitting in the mash itself.
A digital thermometer is really helpful, though not needed. It helps you keep the mash below 212 degrees F, the temperature that water will become vapor, but still warm enough to keep that alcohol turning to vapor.
Then you will need some sort of mash, wine or beer. Something with alcohol. You can use some old wine, such as this that has gone skunk (accidentally got frozen and now tastes bad). You can use beer, such as if you buy a half barrel and can't quite finish it before you have to get the barrel back to get your deposit. You can use your homemade wine that didn't taste quite the way you planned. You can use sugar water that you put yeast into to ferment it. Really, anything with alcohol that isn't already concentrated can be used.
Clean all you parts (except the mash, of course) very well, then either pour boiling water over them to disinfect them or slosh some bleach water (1 part bleach to 4 parts water) over them and then let them air out really well to get that bleach smell out of them.
These are all you should need to distill small amounts of alcohol. I'll come back to show how to put them all together. Again, don't do this unless you are licensed, because what I am about to show you would be illegal to do and we are all such good people we would never go against the government. ;-)