On the subject of distillation, roughly speaking, what I've learned...
How it works: You start in a similar way to making beer: ferment something. Then you take your liquid-grain-pulp-etc mash, after it's fermented a bunch (let's say 10% alcohol) and you pour it into a distillation device, which is basically a pot with a tube on top, which might have stuff in the tube. Heat the bottom, slowly. Liquid comes out (say, 25% alcohol). Non-liquid remains. Keep the liquid, dump the wet remains (or turn it into bread, or feed it to pigs). Next, put the liquid back into your still. Again, heat it slowly. Collect the liquid in small bottles, swapping often. Methanol boils first. Then ethanol. Then higher alcohols (propanol, butanol, etc). The first and last bottles are terrible - mix them together and use them as industrial-strength cleaner, solvent, engine degreaser. The middle stuff is decent. You can take the middle stuff and run it through the still again and again, keeping the middle each time. Eventually - depending on your setup, it could be after the 2nd distillation (1st being 10% to 25%, for example), it could be after your 10th - you will like what you've distilled. You then either drink it, or age it, or infuse it, or distill it through botanicals (to make gin, absinthe, etc), or combinations of the above.
Quality: You don't pay taxes, so it might be cheaper, it might not. Regardless, you can make absolutely brutal cuts, meaning keeping only the best stuff. It would be very expensive for a commercial distillery to do this, so you can end up with vodka so good it tastes just like water. Or, you can fuck up, and leave in too much methanol, and poison yourself.
Dangers: One, you are dealing with aerosols / gases of extremely combustible material; two, you are dealing with poisonous material. Both can fuck you up.
Also: You don't pay taxes on this.
Those are three good reasons for home distillation to be illegal. Realistically, #3 gets you in serious shit - start selling home hooch and you'll be fucked by the law soon enough. #1 and #2 are the no-harm-no-foul reasons; if you do things right, and just give the stuff away, nobody really cares, unless you do something blatant like post the still for sale on craigslist...
Oh, and if you're thinking of aging liquor, it's very hard to do well on a small scale. Vodka? Easy. Ditto white rum, blanco tequila, white rye/bourbon, eau de vie (white brandies of grapes, or other fruit). Gin? Not bad. Absinthe? Okay. But if you want to keep stuff in barrels, you either use small barrels - which means your spirit is over-oaked but still young-tasting, in other words, unbalanced - or you use properly sized casks, which are expensive to fill (240 liters for a full hogshead). Not only that! Aging means angel's share; that is, some liquor leaks through the cask, some evaporates. A good distillery has a cooperage, where professionals deal with barrels; they ensure the angel's share is not too great. Doing it alone, eh, you're going to lose a lot. For example, bourbon might lose 5-10% a year, scotch 2%, rum or tequila might be 20%, doing it yourself you lose probably 50% per year which means three years later 240 theoretical liters are now only 30! Also, warehouses are better at storing the stuff, to ensure random barrels don't fail - you can spring a leak and have your liquor gone in a week if you don't notice. And they can naturally get high temperature swings on top levels, or they can do a good job of faking it with climate control, whereas you won't get those benefits. And they're insured against fire, theft, accidents. So people do age their own, but frankly it usually tastes kinda crappy. You have to create a mash bill that works very well with small casks and short aging periods. On the plus side, you get way more control in the spirit you make, if you know what's up.
Instead of distilling with heat, you could also freeze distill... that may work depending on what you're distilling, but it won't taste very neutral, and the astute among you would notice it doesn't do a very good job of separating heads and tails (methanol and higher alcohols) from the middle.
The shape of your still, and the number of times you distill, will depend on the type of spirit you want. Neutral spirit - whether grain or otherwise - loves column stills, which can spit out 90-95% pure ethanol with very little residual taste. Neutral grain spirits are usually the base of things like gin. On the other hand, aged spirits like various whiskeys should be done in a pot still, which spits out much lower proof with much more organic compounds - esthers, aromatics, etc - the stuff that smells and tastes like whisky without the oak. This stuff can be drunk without aging, or aged for a short while, or a long while if you have the money. You will note that the same base ingredient - grain, for example - can be distilled to be more neutral or less neutral. Same with sugar cane / molasses (rum), agave (mezcal/tequila), fruit (brandies). However, aging neutral stuff... will taste like ethanol and oak, usually, not a good combination.
You might also notice a lot of white whiskey on the shelves of a larger liquor store. This is because we have a lovely micro-distillery boom. We've never had more choice in the spirit we can buy. A micro distillery takes about a million dollars to start up and operate, but it needs cash flow soon after to sustain itself. Therefore, it produces vodka, gin, white rum, etc - stuff that can be sold without aging. It also produces white dog (white bourbon, rye, etc). A big distillery takes white dog and puts it in a barrel; a small one needs cash flow NOW so it will sell some of it to operate and age the rest. Hopefully several years later it has good aged product to sell. A lot of them also take short-cuts in bringing their spirit to market (small casks, pressurized liquor through oak, all sorts of "aging accelerator" bullshit), or buy from a contract distillery and market under their name. Hint to the wise: don't buy white dog at a store, it's a rip off, unless you want to support that distillery specifically. Also, a lot of big distilleries have jumped on the bandwagon - jack daniels sells a white rye for $40, the same price as their single barrel JD offering, which by the way is fantastic despite the jack daniels name and rather terrible quality of their standard lines. This is just a cheap way to get money from whiskey hipsters and ignorant people.
Hope that was interesting to folks.