Finely grate the beetroot and squeeze out as much juice as you can. The mixture for the marinade should be on the dry side.
Add the dill, salt, and sugar to the beetroot and mix well. There's no reason not to use your hands.
Line a sealable container with aluminium foil or clingfilm and fill with one third of the marinade. Place the salmon on top of this mixture skin side down, cover with the remaining marinade and press down. Seal the container and leave to cure for three days in the fridge.
Following the above, shake the mixture from the salmon and cut with a sharp knife into the thinnest slices you can. This may be served on its own for, say, a New Year's Eve spread, or with a buttered baguette.