Turn off the power to the circuit that provides electricity to the recessed lights at your main electrical box. Go into the room where the lights are located, and test them with the light switch. If they turn on, return to the main box and kill the power to the correct circuit, and test them with the light switch again. When the lights remain unlit when the light switch is on, remove the light bulbs from the cans and test the sockets with a voltage tester to ensure that the circuits are dead.
Pry the trim for the recessed lighting off the ceiling.
Remove the cans from the ceiling by releasing the clips on the sides for the can that hold it against the ceiling. Do this by sliding a screwdriver up against the clips to release them. Slide the cans out of the ceiling.
Remove the cover plate on the box attached to the can that contains the wiring. Untwist the plastic connector caps and separate the wires for the light from the wires in the electrical cable leading from the light switch. Loosen the screw that holds the electrical cable in place, and pull the cable out of the box. Lower the light fixture to the ground.
Remove the rest of the light fixtures, using the same process. Pull the cables that run between the different lights out of the ceiling.
Trace the bottom of the lighting cans onto the ceiling where you want to move the lights. Cut holes in the ceiling with a drywall saw.
Cut 12/2 electrical cable for the lights, if needed. If the distance between the lights is the same or less as the original setup, you can reuse the original cables; if it's longer, cut new lengths of cable to fit. If you're moving the lights closer to the light switch, you can cut the cable to fit your needs. If you're moving them farther away, cut an additional length of cable to fit between the end of the cable and the closest hole for the new lighting setup. Connect the original cable to the new cable with plastic connector caps, matching the wires by color.
Connect the wiring for the lights with plastic connector caps. Connect like-colored wires -- black-to-black, white-to-white and the bare copper wires together. Tuck the wiring inside the metal box on the side of the fixture, and screw on the cover plate.
Slide the light fixtures into the holes in the ceiling, and lock them into place by pressing the clips on the sides of the cans out with a screwdriver.
Install the trim for the light cans, and screw in the light bulbs. Restore power to the circuit, and test the lights.
Patch the holes in the ceiling where the lights were originally placed by cutting pieces of drywall to fit the holes, and placing joint compound and drywall tape over the joints to secure the drywall patches. Prime and paint the patches.