Put  about 2 tablespoons of oil or 3 to 4 tablespoons of butter in a skillet.. 
Slice up one or more onions and  spread them out on the bottom of the skillet. 
Put it on medium to medium high heat. Lower if  using butter, it tends to burn easily on higher heat. 
If you have many to cook, you can use several skillets or carefully stack them in the pan but lower the heat and move them in the pan frequently.

If you are using  frozen Varenyky directly from the freezer, add a little water to the skillet and cover until they are soft.  Then, place the Varenyky directly on top of the onions. Do not stir. The onions will keep the dumplings from burning, but will still be close enough to the bottom of the skillet to allow slow cooking.  After about 5 to 10 minutes, they will turn a light golden brown on the bottom. Using a plastic spatula , flip the Varenyky over and cook until the other side is golden. 

Serve immediately while they are hot, smothered in onions and butter. Top with a little sour cream or sprinkle with a little bacon. Melt in your mouth goodness that is truly a fantastic Ukrainian culinary experience.