Hi Sandra, 

Yes, the National Center for Home Food Preservation has a great article on making cider vinegar from fresh pressed apple juice. You can read the full piece online here, but the key process is on the last page. 

Make sure to use good quality apples to start with, and avoid any "dropped" or "windfall" apples picked up from the ground. These apples are more likely to have spoilage organisms on them that could ruin your fermentation. After you press your apples, you pour the juice into a dark crock or jug and cover tightly with a cloth to keep fruit flies out. Bacteria and yeasts naturally on the apples will start the fermentation process. It may take up to 6 months for your juice to turn from juice to hard cider and then eventually into vinegar. Start checking for your desired flavor after about 4 months. 

You will notice that a "mother" starts to form on the vinegar over time; it is a jelly like layer that is cream or beige colored. This is completely normal, but if you see any other colored yeasts or molds growing, you should discard the ferment and start over with fresh juice.

You can store your apple cider vinegar in clean bottles and refrigerate it, but it's recommended to first pasteurize it by heating to 170 degrees Fahrenheit and holding it at that temperature for 10 minutes. 

One last note: homemade vinegars should not be used for canning processes. Because the acidity level is variable, you cannot guarantee that the vinegar will be effective enough to keep your pickles or chutneys safe when canned.

Thanks for using Ask Extension!

Jared