You need to bisect the angles. If the walls to which you want to fix the skirtings are at 100 degrees to each other, for example, then both pieces of skirting need to be mitred at 50 degrees. If you don't bisect the angle (i.e. divide it in 2), the cut surfaces will not be the same length and the joint will not be flush.
You can either :
(a) get a carpenters sliding bevel (i.e. an angle gauge) and gauge the angle between the walls and then measure the angle on the sliding bevel with a protractor. Divide this number by 2 and then use the protractor to set this new angle up on the sliding bevel. Transfer this angle to the timber to be cut (both pieces).
(b) do same as in (a) with sliding bevel but instead transfer this angle to a piece of plywood. Mark out angle with pencil on the plywood. Bisect angle. To do this, measure out say 4" (the distance doesn't matter as long as its the same on each arm) along each arm of the angle to be bisected. Draw a perpendicular to each arm of the angle at the 4"(say) points - these perpendiculars will intersect. Draw a line through this point of intersection to the point of intersection of the arms of the original angle. This new angle is your mitre cut.
method (b) avoids having to put a number on the angle at all.
This can be applied to things like dado rails on stairs etc.
JD, October 2008