Before you lay the cable, clear the path in the walls. For plaster walls, use the claw end of a hammer to score a horizontal line for your path. Underneath the plaster, break, cut, or pry back the lath strips along your path. Doing so will reveal the studs and fireblocks that you'll have to drill through.
You can drill a path through the centre of your studs, headers, fireblocks, and other beams with a ¾-inch or 1-inch paddle bit.
For sheetrock walls, use a sheetrock saw to cut a 5-inch strip parallel to the baseboard. (You might be able to cut multiple, smaller holes and then use a hanger to pass the wire along, but in any event you need to get to the studs.)