Pat dry the shrimp (this will help with the sear).
Lightly salt and pepper shrimp.
Bring a medium sized pan to medium high heat.
Add butter and melt. Add olive oil.
Place shrimp in a single layer into the pan and cook for 1 ½ - 2 minutes or until one side is seared. Don't disturb the shrimp before seeing a sear on the bottom side.
Flip shrimp and cook for 30 seconds - 1 minute or until shrimp is cooked through. The second side will sear faster than the first and doesn't need as much time unless the shrimp are biggens.
Salt and pepper to taste and a squeeze of fresh lemon if desired.
Notes
This is a basic simple recipe for an easy and fast dinner. Add some garlic or herbs or spices as desired.
Use a non-stick skillet. It's just easier for seafood and meats with not a lot of fat. It's easier to learn, easier to cook, and easier to clean for most of us. Non-stick pans are more forgiving.
Don't crowd the pan. Use a pan that's appropriate for the amount of shrimp. 1 pound of peeled and deveined shrimp will fit nicely into ~ 10" - 12" skillet.
Don't like peeling and deveining shrimp? Buy them already done. Most grocery stores will also sell cooked shrimp which would work for this recipe.