The way I cook ribeyes is to put a cast iron pan in the oven and preheat the oven to 500 degrees. (With the pan inside.)
Steaks should be chilling out on the counter for at least 30 minutes to come to room temperature.
Once the oven has preheated, carefully take the pan out and place on the range at a very high heat. Slather the steaks with some olive oil (Or canola, whatevs), add kosher salt, black pepper, and any other seasonings you prefer. (Though I keep it simple with just S & P)
My ribeyes the other night were about an inch thick, maybe slightly under. I placed them both in the screaming hot pan on one side for about 30-40 seconds, did not move them. Flipped them over for another 30-40 seconds, immediately placed into oven.
Cooked them for about 2 minutes on each side then took them out and covered them with foil and let them rest for a few minutes.
As they rested I put a little butter into the pan, swirled it around to scrape up the drippings, then when I uncovered the steaks I put a little butter onto them and served.
Ribeyes were a beautiful medium rare, and delicious.