Save your mother! That's what you'll need to do if you want to make your own vinegar from wine. The mother, or Mother of Vinegar, is that slimy film that forms in vinegars and is needed much the same way that starter is used in bread making. The mother is a nasty looking thing. To be blunt, if vinegar could have a head cold it would look like this. But, you can't make vinegar without its necessary bacteria.
We don't always have any remaining dregs of wine as we can easily knock back a bottle with dinner. But we managed to save a glass here and there of some really fine reds and dumped them in to join their new mother. The relationships are developing quite nicely, I must say. It's hard to say when exactly your vinegar has fully ripened and is ready for use. It was recommended to me that I wait until the mother has sunk to the bottom of the bottle. Then strain the liquid through layers of coffee filters. The last batch turned out wonderfully and we used that mother for the current batch.
The results are delicious, especially if you vary the types of wines you add. Just don't use any sweet wines such as port or sherry. And, even though you may gag a little in the removal, save your mother!
For an exceptional reference on vinegar making check out The Gang of Pour.