Place the vinegar and the apple cider in a crock or jar. Make sure the crock does not have lead-based paint and is food grade. It should hold at least six cups with enough extra room for air circulation.
Cover the opening with a cloth or cotton tea towel. Place in a warm spot (68 to 70 F) for 1 to 2 months. Check it occasionally and sniff it. It will gradually take on a distinct vinegar smell and you will notice a slight film (the culture) on the top.
When the mixture tastes and smells like vinegar, pour off all but 1½ of the vinegar saving some to make more vinegar if you'd like. Place vinegar in airtight bottles.
With the rest of the vinegar which now has the mother culture, add 4 ½ more cups of fresh apple cider to start the process again. The process will take less time, so check it often. Mine has been done as soon as two weeks. You can also bottle all of it if you don't want to make more vinegar.
Once it’s bottled, you can store your vinegar wherever you like. It is shelf-stable and will last for 1-2 years. Over time, the flavor and acidity will mellow out. But it’s so good, you probably won’t be able to keep it around for long!