Plants are pretty robust. I wouldn't worry about simply shaking the clay off the roots. Make sure that you dig a hole that is twice as deep and twice as wide as the root ball. I also like to make a little mound at the bottom of the hole and lay the roots around the mound instead of the usual "just throw it in the hole" technique. This allows the roots to spread in a uniform manner.
Also, obviously you are not going to bury the trunk (what with a hole that is twice as deep as the root ball) so, back fill the hole with some good soil (compost, well rotted manure and so on) until you've reached the depth of the root ball and then, plant your tree.
I also like to water the hole then, after the tree has been planted, water the tree.