Shown here, from a top view, is the miter cut. Each baseboard is simply cut at a 45 degree angle with a miter saw. Theoretically, you can cut baseboards with a manual saw and miter box, but it is much easier to do with a power miter saw (often called a chop saw).
It doesn't matter what kind of profile the baseboards have (profile is the shape on the face). As long as each board is cut at 45 degrees, the two profiles should meet exactly.