Use an all purpose cleaner and the two bucket method. Use one bucket for your fresh cleaning solution and the second bucket to wring your dirty water into. You can either use a sponge or the Don Aslett’s Mini Pro with a Wet/Dry Mop Pad.
Vacuum the baseboards regularly to remove dust before it gets cemented on. If the baseboards are already grimy, use a heavy duty cleaner like our Soilmaster with a White Backed Scrub Sponge to remove the dirt.