How to correctly varnish/lacquer all sides of a countertop?
What I would do is set the top vertical and varnish it as much as you can without varnishing the floor. You'll get about 90% of it done.
The simple path
Let it dry, flip it over and varnish it on the side you couldn't get. Requires nothing special, only time
The complex path
If it has to be done all at once (or you ever want to do this again), you'll need 1x4 boards (scrap boards if possible) or something similar in size. You could also use some old plywood, provided it's at least as large as the countertop. I find a couple of 1x4s would be cheap, but I have no idea what they run in Poland. You'll also need some 2 inch (50mm) nails. Lay the boards down across a sawhorse or some other support and drive the nail heads flush (the nails should be sticking out the other side). Put one nail every 2-3 inches (5-8cm).
Now, varnish the inside and bottom edges of your counter. Set the nail-boards so the nails are facing up. Now, take your counter and carefully set it on the nail boards so the bottom edges are resting on the nails. It would be a good idea if you secured the boards somehow (say screw a cross-brace between then), but it's not hard to set it on them just resting on the sawhorses. The nails will support the counter while you finish the top. It's unlikely anyone will scrutinize the bottom edges.
This setup also has the advantage that you have easy access to use a sprayer if you want