Cover beets in water in a large sauce pan. Bring to a boil for 45 minutes to an hour, depending on the size of the beets. Once they are done boiling, they should be able to be pierced with a fork easily. Drain water and remove skins. I do this wearing kitchen gloves (otherwise your hands will get stained). Rinse the beets under cold water and gently rub the skins off. Slice up the beets after skins are removed, making sure the stems are removed as well.
In a small bowl, combine olive oil, red wine vinegar, rice vinegar, salt and pepper. Mix and pour over sliced beets. Gently toss beets and top with feta cheese.