Method
Cook the beetroot
Roast or boil the beetroot until a knife goes through without resistance.
40m
Peel and cube
Peel while still warm, which is far easier than cold, and cut into cubes.
Dress it warm
While the beetroot is still warm, toss it with olive oil, the vinegar, salt and pepper. Warm beetroot takes up a dressing in a way that cold beetroot does not, so this is the step that decides whether the salad tastes of anything.
Add the onion
Add the thinly sliced red onion. If you want it milder, rinse the slices briefly and pat them dry first.
Cool a little, then finish
Spread the beetroot over a plate to cool it faster. Add the crumbled feta and the chopped parsley or dill.
Taste, and adjust the salt and the vinegar.
Notes
The quick version: leave it a minute and eat it warm, accepting that the feta goes soft. Worth it.
This one says nothing about equipment on purpose, because boiling and roasting both work and the recipe format cannot yet say "either of these".