The anime had shown a lot of evolutions, some appears to be almost instant while some are shown wherein the Pokémon is experiencing some sort of pain. The thing about Pokémon evolution is, it's not entirely based of Darwin's theory. There is no natural selection, survival of the fittest mumbo jumbo. It's actually more of a metamorphosis.
Does it hurt? I think it does. Imagine yourself, every bone in your body growing in an accelerated rate, your skin stretching to accommodate the bigger size of your insides, and a complete overhaul of what you look like in just a matter of seconds. That sounds like it hurts. However, since most in most evolutions the Pokémon doesn't howl in pain, I would assume that they undergo some sort of pain-killing process to bypass their brain's nerve receptors (if they have it).
When it comes to what actually causes a Pokémon to evolve, it's a mixed bag. In all the canons, evolution is hinted when the Pokémon is exhibiting bioluminesence (I would assume it is bioluminesence because surely the Pokémon's body could be emitting some sort of chemical that reacts to something very abundant in the atmosphere thus producing light). I think when a Pokémon wins in a battle and gains experience points, those experience points are converted into energy that when accumulated enough triggers a chemical reaction inside the Pokémon's body thus causing evolution. Those who evolve through other means obviously have a different chemical formula and requires more than just experience points in order to trigger a chemical reaction.
Trade evolutions must have been man-made since anyone could just trade pokeballs personally. They added a new requirement into the formula that only the trading machines can emit, which completes the chemical requirement to trigger a chemical reaction inside a Pokémon's body.
I think the everstone acts as a magnet that attracts the required energy to evolve and absorbs it, hindering the evolution of its holder.
These, of course, are all hypothetical. I just think that chemical reaction fits with the metamorphisis-like evolution of Pokémon.