Fully extend the utility knife's blade. Gently press the tip of the blade between the top of the baseboard and the wall to break the line of paint that binds the wall and baseboard. Run the knife along the top edge of the baseboard to cut through the paint; if you pull baseboard without breaking the line of paint, the paint might peel or crack and cause noticeable surface damage.
Move to one end of the piece of baseboard that you're working on. Shimmy the flatter end of a pry bar between the wall and the baseboard. Gently pull the exposed end of the bar toward your body or twist the pry bar back and forth in a rocking motion. Pull or twist until the nail that holds the baseboard in position is pulled from the wall framing.
Move roughly 12 to 18 inches away from the popped nail. Shimmy the bar behind the molding and pull or twist to pop the next nail. Continue across the baseboard until you reach the opposite end. If possible, remove the entire baseboard by hand. If the baseboard resists, return to the first end of the baseboard.
Place a scrap wood block against the wall and butt pry the bar's curved end against the block. Align the pry bar with one of the nails that holds the baseboard to the wall. Slip the edge of the pry bar's curved end between the baseboard and the wall. Push the pry bar's handle up to force the baseboard nail out of the wall framing. Use the curved end of the bar to pry the baseboard at the remaining nails.
Remove stubborn individual nails with a finish hammer, cat's claw, or pliers. After using a pry bar to pop nails from the baseboard's surface, grip each nail head with a finish hammer's claw, a cat's claw's curved claw, or a pair of pliers. Rock the hammer or cat's claw to gently pry nails without damaging baseboard. If you are using pliers, pull the pliers directly away from the wall to remove the nail.