For a tight fit, you should only measure and cut a skirting board after fixing the adjacent one in position. What’s more, neatness dictates that the ends have to be cut in the right way.
External corners are always mitred. You can use either a deep mitre or box, or a circular saw which should be set to a 45° bevel, and drive light nails through the completed joint. Where walls meet at odd angles (eg, round bay windows) you’ll have to gauge each angle with a sliding bevel, and measure it with a protractor. Then re-set the bevel to half the angle, and mark the pieces accordingly.
On internal corners, however, a mitre will tend to separate and show a gap because, when you fix the second board against the wall, it will tend to move away slightly from the first board. The answer is to scribe the profile of the molding onto the second board — see opposite. Cut it out so that its end fits snugly into position over the first board. Then cut it to length at the other end. (Plain boards, of course; can just be butt-jointed.)
The fixing itself depends largely on what’s behind the old skirting. If it’s fairly recent, the plaster will probably run right down to the floor, the skirting being simply nailed on top of it. Nail the new piece on in the same way, using masonry nails long enough to pass through both layers of plaster and into the brickwork — say 63mm (2 1/2in).
For a hollow timber-framed stud partition, use ordinary oval or lost-head nails, making sure they pass through the cladding and into the timber sole plate (into the studs. too, in the case of wide skirtings). Ordinary nails will also do for solid walls of soft blocks.