Here is what I do for borscht:
Chop a bunch of beets, carrots and potatoes. (I have also added turnips and kohlrabli to this mixture). Whatever proportions you like, but heavy on the beets. Put the mix in a pot with some water and tomato sauce (I use home canned, but you could use the store kind run through a blender.) I add enough to make the soup kind of tomatoey, but not too much.
Then saute onions, celery, and maybe a red pepper, zucchini or whatever.