You can find loads of items on the internet that tell you how incredibly easy it is to make your own Apple Cider Vinegar, and I can't comment on how effective they might be.... but I can share how we make our commercial ACV and hopefully you can adapt for yourself.
You will need patience. Lots of it. It will be a long wait before the vinegar is fully matured and ready for use.
Step 1 - Choosing the correct apples.
It may sound simple, but you need to choose your apples carefully. You need fresh apples, not from a supermarket chill house, and free from fungicidal sprays. So you need to be looking at apples that are spray free, and available and available at harvest.
Cider apples, or cooking apples rich in tannins will deliver the best tasting vinegar by far, so if you are lucky enough to find some bitter-sweet or sharp apples then you are in for a taste sensation.
Step 2 - Choosing the correct water.
We use filtered rainwater in our ACVs, as we are lucky enough to have crystal clear air in the Great Southern region. If you only have tap water, then let it stand, and stir it to let the chlorine escape... or buy some cheapo spring water from the supermarket.
Step 3 - The first brew to Alcohol.
So you have your apples.... Next step is to grind them up, or smash them to obtain a pulp. Don't worry too much about scrubbing them clean, a light wash to remove dust is all that is needed. One of your key ingredients is on the skins of your apples - and that key ingredient is the natural yeast.
Depending on how many kilos of apples you have, and how much residual sweetness you want in your vinegar you need to prepare a sugar solution. The type of sugar is up to you. It could be raw sugar, refined sugar, molasses, or even honey, but what you do need to provide is slightly more basic sugar than is in the apples that you are using. Let's say you are using an apple with about 12% sucrose content..... then aim for around a 15% sugar solution, so that would be 150 g of sugar in a liter of water. You can add this to your apples at equivalent weight, so for a kilo of apple pulp, you can add a kilo of water.
Put your apples and sugar solution into a sealed fermentation container with an air lock. This stage isn't aerobic, and there will be lots of carbon dioxide created as the natural yeasts convert the sugars in the apples and the sweet liquor you have made.... if you get air into it at this stage the fermentation will slow down or stop too early, and you want the natural yeasts to build up your alcohol content. (The beauty of using natural yeasts is that they will stop working before all of the sugar has been converted to alcohol, leaving a hint of residual sweetness.)
The ferment will be active for up to 4 weeks. (We leave ours a full two months after the vigorous bubbling has stopped to let the liquid fully fully absorb all of the apple flavours.)
Step 3 - The Oxidation.
This is where it gets really funky, and if you can't get hold of a culture of "the mother", then you cross your fingers that she's already sleeping in there, ready to wake up.
Decant, and then Strain / filter / press decant by whatever means you have to remove the pulp, but be sure to leave the fines and some cloudiness in the liquid.
Place the liquid into a container that you can easily aerate. Aeration can be as simple as stirring every day, or you could use aquarium air pumps to feed air.... And make sure you regularly feed the air into the liquid, because you now need to slowly oxidise the alcohol and change it to acetic acid....
As the acid develops, so should the mother. I have seen it described as a lace filigree on the top of the liquid.... ours is slightly more aggressive than that, being a 5 mm thick mushroom that develops and floats on the top of the liquid in our barrels.
After a minimum of 6 months, the alcohol should be converted, and you will have an ACV. Vinegars should be a minimum of 5% acid, and yours could be 8% to 10%, so if its too puckering then simply dilute with water. Or enjoy the concentrated fruitiness of a real ACV.