I make it in a very big crock, you can use anything but it should be glass or stoneware, not metal or plastic. And the wider the mouth the better for collecting the yeast from the air.
We used to get windfall apples every year and I would use the bruised and battered ones for vinegar But now I get them where ever I can and just mainly use the scraps.
I cut up as many apples as I have to spare and grate a few to start. Seeds, cores, peels and all. I've also learned that for some reason if the scraps are allowed to oxidize (turn a bit brown) the flavor of the vinegar is better. But you can make it without letting them oxidize.
Put them in the container and cover with well water (if you have city type water then you'll probably need distilled water because the chemicals will kill or retard the growth of the Mother). Cover the mouth of the container with a couple of layers of cheesecloth (to keep out bugs and stuff) and secure with a string or a rubber band. You can continue adding fruit the whole time. Peels, cores, even juice (as long as it's not processed. processed juice or anything can kill the Mother). When the Mother forms you can stop adding and allow it to just ferment or keep adding but it will take longer. The Mother is the scum that forms on top. Do not remove the Mother until the vinegar is completely done to your preference.
You can start testing right away but the longer it sets the better it is. If it's really hot I start testing at 2 weeks, in the winter it can take 2 months. To test just dip out a tiny amount and taste it.
Pears in the crock
If you want straight apple vinegar then just add apples otherwise you can any fruit bits you want and make a fruit vinegar. Or you can make different vinegars for different things. Pear vinegar is very good!
You can save the Mother by keeping it in a jar of vinegar if you're going to use it to make more soon.
We use a lot of vinegar ... for the animal waters, hair rinse, cleaning, cooking, laundry rinse, windshield wiper fluid, window cleaner, general cleaner and more.
Someone recently asked about using homemade vinegar for canning. I honestly have no idea at all. I don't know much about canning but I believe the acidity is what's important and homemade vinegar would vary in acidity without some way to test it.