The best way to do it is cut drywall and patch. Are you going parallel to the joists? If so, you can cut some rectangles and route the wire that way. If you are going parallel to the joists, then you have to drill through each joist, which means taking down a long section of drywall.
If you happen to have remodeling style recessed lights that means you can remove the fixture, let it dangle from cords and have existing holes you can reach up through. If they are new construction cans your best bet is the cut and patch route.
If you hire a really good professional wiring guru he will have a drill setup capable of cutting with a long flexible drill bit shafts and can minimize the number of holes required.
All of our recommendations are without knowledge of the nature of your room or it's original construction.
Good point about the remodeling type of recessed lights, Big. I never think about those. Another possibility is to add crown molding and run the wires there or remove trim and run the wires there. But these all depend on what the room looks like and where you're trying to go with the wiring.