I have a roughly 14" * 14" hole in my ceiling, after an electrician put a junction box there. The box is a flush 10x10 box, and I want to be able to remove the lid later. The lid right now is close to flush to the bottom finished side of the 1/2" drywall. I don't have a lot of experience with drywall, and I'm especially puzzled on how to make a nice transition to this box (which does not have a mud ring). I could cut back the sheetrock a bit on each side to expose half of the joists. Would you recommend one large piece of drywall with a hole cut for the box?
The problem is that it's a textured ceiling and that would be hard to match if you cut back to the joists. You probably won't need to remove the lid to this box very often but it does have to be accessible. Have you thought about just attaching a 14"x 14" or 16"x 16" register over the box? It would make it less of an eye sore but still be accessible. Maybe use magnets like Jasen commented on.
Something like this:
You need a flush mount cover for that box
What your electrician did was install a standard NEMA 1 (indoor) enclosure/pull box there, and these by and large come by default set up to be surface mounted with their back to a wall, for use in industrial applications and utility spaces. However, for a finished application, you need to fit a flush mount cover of the correct size to the box instead of the stock surface mounted cover. It looks like you'll also have to unmount and remount the box, with the breaker for that circuit or circuits off, so that it is actually flush with the finished surface, instead of being recessed slightly, as the flush cover won't fit properly otherwise.
While JACKs suggestion disguises the box well and removes the need for drywall work, it also is a potential code violation and makes it so someone in the future might not even know the box is there (it will look like a return air vent for an hvac system).
That said, they make code-friendly covers called "Access Panels" explicitly for this purpose--you can even buy ones with spring clips that allow the panel to be secured directly to the drywall so you don't even have to figure out how to fasten it in place. This solution might not blend in as well as a return air grille since return air ducts in ceilings are more common, but access points to electrical boxes also shouldn't be hidden.