Bring a large pot of water to boil, add the potatoes (whole, unpeeled), carrots (whole or cut in half, unpeeled) and cook on med-high heat until potatoes and carrots are cooked through, about 45 minutes. You can poke the potatoes/carrots with a fork to see if they're soft and cooked through. Once cooked drain out water from the pot and set potatoes/carrots aside to cool. Meanwhile move on to steps 2 and 3.
Bring a medium pot of water to boil, add the beets (Whole or cut in half if they're large, unpeeled) and cook on med-high heat until cooked through and soft, about 45-55 minutes. Once cooked, drain out water from the pot and set beets aside to cool.
Put eggs into a small pot, cover eggs with water and bring to a boil. Cook until eggs are hard boiled, about 10-15 minutes, then drain water out of the pot. Peel the eggs once cooled down and set aside. (I've found that the longer you wait to peel the eggs, the harder they will be to peel).
Cut the smoked salmon into small pieces. In a (16x3) casserole dish (or any dish you prefer) layer the smoked salmon in a single layer around the bottom of the casserole dish.
Once your potatoes have cooled down, peel the skin off, then grate them with a grater and sprinkle over the smoked salmon pieces. Sprinkle a little bit of salt on the grated potato layer. If using herring instead of smoked salmon then no salt is needed as herring is usually already very salty.
Sprinkle the finely chopped sweet onion over the layer of potatoes. Then add about 3/4 cup mayonnaise over the potato/onion layer and carefully spread it around to cover the entire layer evenly.
Peel and grate the beets (some people prefer to use kitchen gloves for this step because beets will stain your hands bright red for a few hours). Gently sprinkle the grated beets over the layer of mayonnaise.
Peel and grate the carrots. Gently sprinkle the carrots over the layer of grated beets. Add another about 3/4 cup mayonnaise over the beet/carrot layer and carefully spread it around to cover the entire layer evenly.
Grate the peeled eggs and gently sprinkle them over the top of the last mayonnaise layer to completely cover the entire salad. Cover the Layered Salad tightly with foil or a lid and refrigerate overnight or for at least 8 hours. Best served cold, right out of the fridge!