Get the biggest pot that will fit on your stove. Fill it with water and bring to a boil. Add some vegetable oil. This will prevent the Varenyky from sticking together when there are several in the pot. You will need this pot to be boiling when you start and continue to be boiling the entire time. Replenish the water when the level drops.. Its a good idea to add a few cups if you are taking a tea break, then it has time to recover. 
 Also, if you made your fillings yesterday and they are still in the fridge, they need to be taken out and allowed to come to room temperature. If they are ice cold, they'll be a little stiff to work with

You will need a pan, or towels set out to receive the hot and dripping wet Varenyky. I use my broiler pan. Perfect to allow water to drain off. Small cooling racks also work well. If you don't have either, set out some lint free towels or cheese cloth. Although, you may have to change it often. 
Set out another pan to receive the cool and dry Varenyky.Use wax paper to separate layers of stacked Varenyky. If you are planning to freeze them, make sure this pan will fit in your freezer. 

Sprinkle some flour on your work surface. Pinch off a baseball size piece of dough. Form it into a somewhat uniform rope, 3/4 to 1 inch thick. It does not have to be perfect. 

With a knife, cut the rope of dough into uniform cubes. 

Pick up one of the dough cubes and roll it into a ball with your hands. 

With your palm, flatten out the ball on your work surface.  You should end up with almost a perfect circle of dough. 
 

With a rolling pin, dowel rod  or jelly jar, roll out the circle of dough. How thick should  it be? It is really something that you have to learn on your own. Too thin and they fall apart when you boil it. (This will be very evident. Your Varenyky will be just a big noodle. A very tasty big noodle, but a noodle just the same.) If you make it too thick, they will be difficult to cook. The outside will be tough and the inside will be raw dough.  It also wastes a good deal of dough and the number made will be much less. It takes practice.

Scoop about 1 heaping spoonful of your chosen filling in the center of the dough, holding it as shown in the diagram. Keep it concentrated in the middle. You will be able to evenly distribute it once the dumpling is closed. Its important now to keep it in the center away from the edges. 

Fold the dough in half, pinching the Varenyky shut along the edges as shown in the photo.  Keep the filling away from the seams. Use your fingers and pinch it firmly closed. The seam should be about  1/4 inch to 1/2 inch  wide. If it doesn't seem to want to stick together, then make sure there is not too much flour on the edges. If they look clean and it still won't stick then your dough does not have enough liquid. Put all the dough back in the pan. Sprinkle a generous amount on the dough and knead it  for a few minutes. Then, try again. 

Pat the Varenyky to distribute filling evenly inside the dumpling. There should be no holes in the dough. If there is , you can try making a little patch.  Double check the seam, it must be sealed or all the filling will leak out. 

Using a wide slotted spoon, lower the Varenyky into the boiling water. Doing it this way, it keeps it from being damaged if it was just dropped into the pot, as well as keeping you from getting burned. Once in the pot, give the water a gentle swirl. This keeps it from sticking to the bottom when it first gets in the water.  We like the plastic spoon better over a metal spoon. The metal spoon has a sharper edge and is more likely to accidentally cut the Varenyky. 

When the Varenyky is completely floating flat on the top of the boiling water its time to use the wide spoon, scoop up the dumpling from the underneath and lift it out of the pot. Allow it to drain for a few seconds. Then lay it gently on the drying tray. When it is cool enough to touch, flip it over to allow the other side to cool and dry. I keep moving them to one side of the tray as they cool. This way, when they reach the end they are ready to move to the final freezing tray.

TIP: Set up a fan to blow lightly over the drying tray, it speeds up the process.

If you are not going to prepare these to eat in a day or two, it is best to freeze them. Once dry, stack them on a cookie sheet or a pan small enough to fit in your freezer. Stack the Varenyky in layers between wax paper. Freeze overnight and then remove them from the pan, placing them  in zip lock freezer bags. Then its back into the freezer until they are ready to cook.