For fresh beets, place them in a medium saucepan with cold water to cover.
Cover and bring to a simmer over low heat.
Cook for about 1 hour or until tender when pierced with a knife, replenishing the water if necessary.
Drain.
(If using canned beets, drain and let dry on paper towels.
) Peel and cut into cubes.
Place in a medium bowl, add apple cider vinegar, and stir to combine.
Let sit for 1 hour.
Meanwhile, place the potatoes in a medium saucepan, add cold water to cover, and salt.
Cover and bring to a simmer over low heat.
Cook for about 20 minutes or until tender when pierced with a knife.
Drain and let cool slightly.
Peel and cut into cubes.
Place the beets in a serving dish or in individual dishes.
Scatter the potatoes over the beets and season with salt and pepper.
Lightly spread mayonnaise over the potatoes.
Sprinkle with the sliced eggs and serve at room temperature.