Trim the greens off of the beets, scrub with running water then place in a medium saucepan and cover with water by about an inch. Bring to a boil then lower the heat and simmer for about 25 to 35 minutes, depending on the size of the beets. They are done when soft enough to be easily poked with a fork.
Next, drain the beets and rinse them cold water. Use your fingers to gently rub of the skin. Discard the skin then cut the beets into quarters or slices.
In a large jar (or bowl with a lid), combine the apple cider vinegar, honey (or agave), olive oil, dry mustard and salt. Place the lid on the jar and shake vigorously. Add the beets to the jar to cover with liquid. Marinate for at least a half hour at room temperature or in the refrigerator overnight. Picked beets will keep for up to 1 week sealed in the refrigerator.