It's a simple matter to run wires through the house framing before the walls are covered over, but it's another matter to do it afterward. Unless you are prepared to remove and replace wallboard, you're better off running wires to the attic or basement, then horizontally from there. You can then fish them vertically through the wall and pull them out where they are needed. Alternatively, you can cut off out small strips of drywall along the path of the wire, drill holes in the studs, run the wires, and replace the drywall.
Remove a small section of drywall near the ceiling or floor, using a drywall saw, to access the attic or basement from an outlet or fixture box. Make the hole large enough so that you can drill a 1/2-inch hole through the top or bottom plate of the wall.
Insert a 1/2-inch spade bit into a drill and drill a hole through the top or bottom plate of the wall. Drill this hole at an angle so that you can keep the body of the drill outside the wall.
Straighten out a coat hanger and feed it through the hole. Have a helper grab the other end and attach the electrical wire to it with tape, then pull the coat hanger back through the hole, bringing the wire with it.
Pull the wire along the floor joists or ceiling rafters until you are above or below the new location, then drill a hole through the top or bottom plate of that wall and feed the coat hanger, along with the attached wire, through the hole. Have your helper intercept the hanger and remove the wire.
Attach the wire to joists or rafters along the lateral run, using wire staples and a hammer
Cut out a 2-inch strip of drywall that extends about 6 inches on either side of each stud along the intended path of the wire, using the drywall saw. Save the cut-out pieces of drywall.
Drill a hole through each stud with a 1/2-inch spade bit, being sure the centre of each hole is at least 1 inch from either edge of the stud.
Feed the wire through the holes.
Replace the pieces of drywall by screwing them back to the stud with drywall screws and a drill. Apply mud over each piece and lay a length of drywall tape over each piece that completely covers it. Scrape the tape flat to the wall with a drywall blade and let the mud dry overnight. Afterward, lay on a topcoat of mud and feather it into the wall to hide the repair. Let this coat dry, then apply another one.
If the wall is made of tile or another material that is difficult to repair, your only option probably is to pass the wires through the basement or attic.
If you have to join wires in the basement or attic, do it in a covered junction box. It is hazardous and a code violation to leave capped wires exposed.