Use a vegetable peeler to remove the tough exterior of the root and trim off the ends of your horseradish; the skin of the root is really tough and you definitely don't want this in the finished product.
Once you have cleaned your horseradish root, the rest is easy. Chop the horseradish into small pieces and put it into a food processor or use the fine holes on a grater to grate the root manually and mix using a mortar and pestle. A food processor is preferable since it is far faster than grating and mixing by hand.
Add water to the processor and chop until the horseradish has been thoroughly blended and has the consistency of a thick paste.
Add the vinegar and salt to the horseradish immediately and mix briefly to blend these ingredients in.
While working with horseradish, don't get too close and keep the windows in your kitchen open for ventilation; horseradish can cause your eyes to tear up and sting easily.
Once it's all mixed, transfer the horseradish sauce into a clean jar with a lid, and put it in the refrigerator.