Martha Stewart and Food Network provide simple pickled beet recipes on their websites. One recipe calls for fresh beets, while the other recipe requires canned beets.
The Martha Stewart recipe requires 6 red beets, salt, 1/3 cup of cider vinegar, 1/4 teaspoon of freshly ground pepper and 1/3 cup of olive oil. Place the beets in a large pot, and cover them with 2 inches of cold water. Bring the water to a boil over high heat. Add 2 teaspoons salt, and then reduce the heat, allowing it to boil lightly.
Cook the beets for approximately 30 minutes or until they are tender. Drain and peel the beets, and cut them into 1/4-inch-thick slices. In a small bowl, whisk together the vinegar, 1 1/4 teaspoons salt and the pepper in a small bowl. Add the oil until it is emulsified, and pour the mixture over the over beets.
The Food Network recipe includes 1 cup of brown sugar, 1/2 teaspoon of salt, 3/4 cup of cider vinegar, 1/4 cup of water, 1 quart canned red beets and juice, and 3 pinches of mixed pickling spice. Heat the sugar, salt, cider vinegar, water, beet juice and pickling spice in a large pot. Allow the ingredients to simmer for 15 minutes. Combine the beets with the other ingredients. Refrigerate the ingredients for 24 hours before serving.