Dahlias are normally divided just before planting in Australia or by a grower prior to selling to check for good eye formation ( this mis where the shoots and stems grow form, like on a potato Dahlias develop eyes
When you divide a large clump of Dahlias you may find some naturally come apart as they are plants that developed their own stem. Otherwise it is a bit different and a good sharp knife and Secateurs will help. The important thing to note is a Dahlia tuber will easily grow as long as their is some stem and end of tuber is intact. Large clumps may have a squishy tuber on outside, simply remove and cut back to clean tuber or stem.
By dividing a good sized clump you can share with friends, increase the flower production and they settle in faster than a larger clump.
Prior to planting dig in well rotted cow manure into soil and let it sit for a few weeks if possible. Use free draining soil and check ph of soil prior to planting especially with newly bought soil.
Just remember when planting resist watering especially when they are first planted, at least wait until good growth above ground is achieved. Place stakes in at planting to avoid tuber damage.
When cutting Dahlia flowers make sure to not leave an open stem, stems are often hollow so cut down until it is sealed and on a angle.