How can I attach PVC skirting board to painted wooden skirting board?

You can use El Pulpito: first, sand the wooden skirting board until all the paint has been removed so that it is absorbent. Keep in mind that both surfaces must be clean. Then apply the adhesive generously in lines or waves to one of the surfaces. Next, position the other element to be attached and press. Finally, immediately remove any adhesive residue with a damp cloth.