Cut Flowers Here's some advice from Swan Island Dahlias:

"Best time to cut your flowers is in the cool mornings. Place the cut stems in 2 - 3" of VERY HOT WATER (approx. 160-180 degrees) and allow to cool at least one hour. This will set your blooms and make your flowers last for 4 - 6 days. Removing old blooms will keep your plants strong and blooming late into the season."

Keep the water in your vase fresh ... either change the water at least daily, or sometimes I'll add a few drops of bleach to the water in the vase.
Cuttings It's easy to propagate dahlias from cuttings.  Here's a link to "February Dahlias" on the Scottish Dahlia Scene's web site ... be sure and click on the various photo links.
Digging To dig or not to dig?  Most serious hobbyists dig every year, and we do with most of our dahlias, but our experience has also been for dahlias left in the ground, we get blooms earlier.  The trick (I think) is to make sure the plant is well protected from frost (mulch) and in well drained soil.  My dad left many of his plants in the ground and he had great dahlias.  Experiment a little and do what works best for you.  If you do decide to dig, take care not to break the neck (portion of the tuber just under the crown).
Dividing Dividing root clumps to get individual tubers can be a little tricky.  A dahlia tuber is similar to a sweet potato, with all the eyes on one end (the crown).  Trim off as much of the stalk as possible, but be sure you keep at least one eye.  If the tubers are really big, a good portion can be cut off.
Growing Guide

Check out this link to the Puget Sound Dahlia Association's guide to Growing Dahlias ... a good source.
Planting Depth Many sources say plant the tubers 4 to 6 inches deep.  I like to plant our tubers much shallower, so the eyes are just under the surface.
Planting Time There are lots of opinions this topic.  Make sure you're into the frost free period for your planting area.  Dahlias will not tolerate freezing.  Most growers in the Pacific Northwest will plant their tubers anywhere from 4/15 through 6/15.
Slugs Slugs like dahlias, especially when they are just beginning to sprout, so you've got to protect.  There are many products available for slug protection, some more toxic than others.  We're not real big on using chemicals in our garden, so believe it or not, we use ducks to keep our slugs down ... works for us!  :o)
Storing I think there are as many ways to store tubers as there are dahlia growers.  Most advice concurs in a cool (40°F), dark environment.  Think root cellar.  Here's a link to one of what I think is one of the better articles on tuber storage.