As the temperature increases the plants become active. The plants are not officially out of dormancy until leaves begin to appear. Most people don't realize that nurserymen can only dig deciduous plants while they are dormant. Once a deciduous plant develops leaves in the spring, it can not safely be transplanted until late fall when it is dormant again. Digging a deciduous plant once it leafs out will immediately put the plant into shock, and likely kill it.
Evergreens are a little different.
They can not be safely transplanted once new growth is established in the spring, but once that new growth hardens off later in the summer, evergreens can be transplanted. Of course, transplanting during dormancy is usually the safest bet. Back to propagating by division. To divide a plant all you do is dig up the parent plant. The entire plant will come out of the ground in one large clump.