I split mine when I can see the new "bullets" or young shoots starting to form. This way you can exactly where to cut and, more importantly, where not to cut.
On smaller plants I find the best tool is an old bread knife which I use to cut as one would a cake, one cut into the middle, then work out to the edge.
Larger specimens can be tackled with a spade. Again, I'd look for a clear line between buds before making a chop. You can take a line from the middle out to the edge, or cut clean across. You really just need to spend a bit of time looking at them from all angles to establish which chunks would work best. I also find it best to dig up the whole clump, if it's in the ground, and work on a hard surface like a path, or slab which makes cutting easier.
It really depends upon the weather when they get to this stage, but I've split them even when the leaves are starting to unfold when I've got " a bid behind".
They're more resilient than they look.