Firstly put a combination of 50% butter (or margarine) and olive oil in the pan.
The butter gives a rounded, gentle flavour without masking the fish's freshness.
The oil allows the temperature to increase without smoking or burning. Oil has a higher smoke point and helps 'keep the show on the road'.
Here are the steps...
1) Add the oil/butter and heat the pan.
2) Then place the fish fillet/s in it, presentation side downwards. If both sides have been skinned, the best-looking side.
3) Turn down the heat to low, so the fat just bubbles or simmers. It's important not to burn the fish. It has very delicate flesh as well as fine flavour. The side that's facing up is then the 'test' area. You press it gently with a finger from time to time to notice it firming up. When it is firm, turn the fish over.
4) Cook the other side for only a short time - that's all it will need.
5) Be sure to have the plates hot/warm at-the-ready. Fish goes cold quickly on a cold plate. Cold food that's supposed to be hot is not nice. And with fish you'd be wasting good food by poor management.
6) Squeeze on fresh lemon and have a spare wedge on each plate.
A thoughtful host cuts the lemon into 4 or 5 and then cuts away the pith strip at the bottom of the wedge. This helps a lot when it comes to inserting the fork and squeezing - the juice goes downwards onto the target and not sideways into your guests' eyes.