Start with: http://www.marksdailyapple.com/how-to-make-red-wine-vinegar/#axzz2ODnXUyFz. This is a fact filled step by step with good pictures of what to expect. The first time I actually SAW mother of vinegar, I freaked a little. I was glad of these pictures! It was supposed to look like that! Also, I found this article comforting as she thought of the movie Aliens, when mother was mentioned to her! http://boulderlocavore.com/2011/02/make-it-yourself-homemade-vinegar.html
So, basically you need, a clean jar, cool storage place, air and wither apple cider vinegar or red wine and water to begin making your own vinegar.
What I really wanted was a tutorial in how to make the apple cider to get the white vinegar from. I use a lot of white vinegar for a lot of different chores. I clean with it, cook with it, use it to set the dye on Easter eggs, and many more uses. I finally found simple and direct instructions at this site: http://ohioline.osu.edu/hyg-fact/5000/pdf/5346.pdf. This included the steps of adding yeast to begin the fermentation and then pasteurization before jarring to store the vinegar.