Ironically, white vinegar (as far as I'm aware) is the harder one to make, as it is a distilled product. White wine/Red wine/Malt/Cider vinegar are all far easier to make. I've made malt vinegar
before and it's come out surpirisingly well!
Failsafe method is actually very easy...
1. Get a large bottle that you want to create the vinegar in. It'll be out of action for a few months, so make sure you won't need it for a while. Wider bottles are better, as they allow more surface area and therefore oxygen transfer, which is required for acetobacter.
2. Fill the bottle 1/2 full with beer. I used a dark mild that I wasn't too impressed with. Something low hopped is good, so the bitterness doesn't fight with the sourness. Allow the beer to warm to room temperature, and then shake to aerate.
3. Look through the vinegars in your cupboard, and see if any have a little floaty cloudy jellyfish in them. The jellyfish is the mother which is what will turn the alcohol into vinegar. I'm told that most vinegar is pasteurised, however almost every vinegar in my cupboard tends to form a mother, meaning that there's live cultures in there. If you haven't got any, you can probably buy a vinegar mother online from a homebrew or healthfood shop, or try tracking down an unpasteurised vinegar. *
4. Fill 1/4 of the bottle with the vinegar (try to include the cloudy mother) so it's now 3/4 full. Put cheesecloth over the top and stick it in the back of the cupboard for a few months.
Vinegar mothers like oxygen and a little warmth, so every so often give it a little swirl to ensure that there's a bit more oxygen getting to it. You'll notice, after a few weeks, that the mother rises to the surface, which is a good thing. Then after a few months you'll have a thick jellyfish sitting on top (as in the picture I linked to). Once it tastes as sour as you like, decant 1/2 the bottle into smaller bottles, refill with room temp beer, and repeat the process.
You can do all this with wine or cider, whatever you'd like. Experiment a little and try different beers. Despite the suggestion above, try an IPA vinegar and see how it tastes! I haven't done it, so if you do, let me know how it turns out!!
* For a hard-core alternative and distinctive tasting vinegar, try sourcing your own mother. Hang a vinegar fly trap out in the open in a shady location during the summer months. Fill the trap with some beer, maybe a splash of vinegar, a touch of fruit. The better the fermenting smell, the more chance you have of attracting vinegar flies. Allow it to sit for a few weeks until it's cloudy, then filter through some fine cheesecloth or a coffee filter. The filtered liquid will contain the acetobacter required to kickstart the mother creation, so just add this in place of the mother for step 4.