I block any quilt that I show after I'm done quilting. Some quilters do it before they put the binding on, but I block mine after I'm done with the binding and the sleeve. Believe me, I don't bother with any of this if the quilt isn't being shown!
I stretch mine out on the floor. If I don't wash it first, I use a spray bottle of water to dampen it. Then I measure the diagonals, and make sure they're the same. Then I measure across the center of the quilt and make sure the sides are straight, and the corners are square. I use pins to hold it down until it's dry - usually overnight.
My quilts are queen size, so a cutting board wouldn't help me. The problem with the Dritz cutting board is that when you get the quilt wet, the card board won't hold. Since I have hardwood floors, I use foam tiles under the quilt so I can pin easily - they're also easier on the knees.
This is a link that describes it better:
http://www.quiltuniversity.com/blocking.htm
Good luck with your fair entry!
Janet