Heat a heavy skillet, and once it's hot, add oil or butter (if using the latter, wait until it has stopped sputtering before proceeding).
Add asparagus, sprinkle lightly with salt, and cook for 1 minute. Push asparagus to sides of pan.
Add trout in middle of pan, skin-side down. Sprinkle flesh side lightly with salt and black pepper; cook for 2 minutes. Stir asparagus about while fish cooks. Test a piece of asparagus stalk to decide when it's done enough for your taste.
Turn fish over, cook for another 40 seconds–1 minute. Remove fish and asparagus from pan, and with skillet still off the heat, add a squeeze of lemon juice to it. Put skillet down on an unheated burner, and use a wooden spoon to rout any little brown bits from the pan's bottom into the tiny bit of liquid. Add a tablespoon or two of white wine or a bit of lemon juice to create a small amount of sauce.
Add butter, stir until it melts, and pour the small amount of sauce over the fish and asparagus.