The drag coefficient is usually given as a funtion of the lift coefficient and the zero-lift drag coefficient ($c_{D0}$):
$c_D=c_{D0}+k\cdot c_L^2$
How can I calculate/estimate $c_{D0}$?
You can look it up in reference books. For wings, the NASA report server is your friend. For complete aircraft, there is some data available in books about pre-design of aircraft. The one I have is Synthesis of Subsonic Airplane Design by E. Torenbeek, and gives the following numbers for $C_{D_0}$
Appendix F of the same book gives a method for more detailed estimation in the pre-design phase, when no wind tunnel data is available, based on data of the components that make up an aeroplane.