Often a wall receptacle from an upper floor can be used as a source for a new ceiling fixture below, but a switch loop must be run to a wall switch in addition to fishing the cable from the source.
By code the junction box must remain accessible, so look for a spot where the cover plate will blend. Use a 3x2½ inch device box like the ones use for wall outlets and set it at the same level as the existing wall receptacles to minimize visual impact.
Decide on the location for the new electrical fixture and where the source will be. Determine inside of which walls and ceilings the cable must be run. For example, with a new ceiling fixture using a source from an existing wall receptacle, the cable will have to be run inside the wall cavity, through the top plate, into the ceiling cavity, and on to the new fixture.
Use a wood chisel to chip out between the two cuts, deep enough to fit the plate flush with the stud surface. Keep the plates flush with the studs to ensure the baseboard won’t stick out when reinstalled.