Working room by room, spray the baseboards with an all-purpose cleaner. Your trusty Handy Andy in hot water would works wonders. Be careful not to soak your baseboards or get too much water on the wall behind them. Let the solution sit for about 10 minutes
Using a damp sponge mop with clean water, wash the baseboards. If the stains are stubborn, just scrub harder, but refrain from using anything abrasive, like a scouring pad, on your baseboards.