I like to do it with a known good scope when I get a new gun. You shoot at a big piece of paper and see where the shot lands.
Assuming your scope is dead on centre with the cylinder/mounts you get an idea of how well centred the barrel is with the cylinder.
If you are lucky your shot will land somewhere in the vertical plane, meaning your mounts and dovetails are in line with the barrel. If you are unlucky and your shot lands left or right if centre, you can try and track down the problem... it could be your mounts, could be the barrel is bent sideways, could be a few things..
To me, centering the scope is just removing a variable, thereby exposing others