If you order borscht in a U.S. deli, you'll generally get a little dish of shredded beets with a dollup of sour cream. Nothing wrong with that, but I have had some success with the following meal-in-itself Russian version, from the N.Y. Times Cookbook:

1 lb lean beef, cubed
1.5 qt water
1 T salt
1.5 c shredded raw beets
0.75 c shredded carrots
0.75 c white turnips
1 med onion, chopped
2 T tomato puree
2 T vinegar
1 t sugar
2 T butter
0.5 head cabbage, shredded
Fresh-ground black pepper
2 bay leaves

Simmer the beef, covered, in salted water until tender, about 1.5 h.
Meanwhile, in a large saucepan simmer the beets, carrots, turnips, onion, puree, vinegar, sugar, & butter, covered, 15 min. Stir frequently. Add the cabbage, & cook 10 min longer.
Add the vegetable mixture, pepper, & bay leaves to the meat & broth. Cook until the vegetables are tender.
Serve with sour cream.