How do I file a motion with the district court that handled my adoption to get the records opened?

You get a GOOD lawyer, and have a medical emergency that calls for it.

Period.

You cannot get adoption records opened just because you want to know. Your birthparents were guaranteed their privacy when they relinquished their parental rights

You can, of course, search in other ways. But I have not heard of ANY court opening adoption records for anything less than a medical emergency.

You will need a reason that is allowed in your state. Merely wanting to know who they are is not normally a reason.