There are a lot of sources on the internet to instruct you, but the one thing you add is "mother of vinegar."

Mother of vinegar is a substance composed of a form of cellulose and acetic acid bacteria that develops on fermenting alcoholic liquids, which turns alcohol into acetic acid with the help of oxygen from the air. It is added to wine, cider, or other alcoholic liquids to produce vinegar.

Mother of vinegar can also form in store-bought vinegar if there is some non-fermented sugar and/or alcohol contained in the vinegar. While not appetizing in appearance, mother of vinegar is completely harmless and vinegar does not have to be discarded because of it. It can be filtered out using a coffee filter, or simply left in and ignored.

If you want to make distilled vinegar, then you would need to distill it.