This process only requires you to cut butter into cubes and take your pan sauce off the heat so you can whisk, stir, or whirl in one cube at a time until melted.
It's important to emulsify your butter into the sauce properly. Otherwise, if done incorrectly, an unappetizing oil stick will be floating on top of your pan sauce.
To prevent the destabilization of the emulsification, slowly add the cold chunks of butter to the sauce off the heat to help stabilize the temperature.
The ideal temperature range for this process is above 85 degrees Fahrenheit (per Cook's Illustrated) but under 180 degrees Fahrenheit (per MasterClass).
Next time you make gravy, try mounting the sauce with butter at the end to thicken the sauce to a rich glossiness rather than an over-starched clumpiness.