I opt for crimini (often called baby bellas or baby portabellas) over white button mushrooms just because I think they have a bit more depth of flavor, but any mushroom will work, so pick what you like.
Heat a stainless steel pan to medium high heat and add extra virgin olive oil and some butter (you can use all oil if preferred, but I like the flavor butter adds). Add the sliced mushrooms and toss immediately to combine, then cook, stirring occasionally until the mushrooms release all of their water (shrinking in size as they do) and brown all over. Do NOT salt at this time, as you need to wait to see what volume of mushrooms you have left after they cook down or they'll be overly salted. The salt also causes them to release too much water too quickly, so they simmer instead of caramelizing.
Caramelizing mushrooms takes some time, so lower the heat to medium or medium low and don't try to rush it. Once the mushrooms are fully cooked and nicely browned, season with salt and pepper and serve immediately as a vegetable side dish, topping for steaks or chops, or mixed into other vegetables such as garlic sauteed spinach or green beans.