One of the most important things to remember when preparing meat/fish is that your raw ingredient should not be too cold when it hits the pan. If the temperature is too low, the meat ends up "boiling" instead of frying.
Therefore, take out the meat well in advance, preferably 30 minutes before.
Sprinkle the fish with salt on both sides, a quarter of an hour before frying it. The salt helps draw the liquid out of the meat and makes it juicier.
Heat a thick-bottomed pan over medium-high heat with oil.
Pat the fish dry with salt; this can be done with kitchen paper.
Place the fillet skin side down and let it fry for 2 minutes.
Add the butter to the pan and give the fish an additional 3-4 minutes on the skin side.
Turn the fish and give it 30 seconds on the other side.
Drizzle a little lemon juice on the fish and serve it with a good flake salt.