Norm Abram's Best Tricks of the Trade III
via This Old House
A: Sure, that's very doable. The key is to make a perfectly plumb cut so that the cabinet's side will butt tightly against the baseboard. All you need is a level, a handsaw, a sharp chisel or a utility knife, a nailset, and a hammer or a screwdriver.
Step 1: Use the level to mark a plumb line on the baseboard (a square is unreliable because you can never assume the floor is level). If there are any nails in the baseboard where the cut will be made, drive them all the way through with a nailset.
Nail or screw a 14 scrap block along the line on the side of the baseboard that will remain. This block serves as a guide to prevent the saw blade from wandering and to help you achieve a clean, straight cut. Tape a thin piece of cardboard to the floor to protect it from being hit by the saw.
Place the blade of a fine-tooth handsaw against the scrap and start the cut, going straight up and down. Once you get a kerf started, turn the blade very slightly so that the cut angles behind the block. This "back cut" helps you get a tight fit with the cabinet. As the saw sinks into the wood, tip it forward so that you don't gouge the wall. The kerf won't go all the way to the floor, so finish the cut with a chisel or a utility knife. Pry off the baseboard on the waste side of the cut, then remove the guide block and fill the holes left by the fasteners. Now the fun begins: installing your cabinet.