How is the zero-lift drag coefficient calculated? 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 $C_{D_0}$


0.014 - 0.020 for high subsonic jet aircraft
0.018 - 0.024 for large turboprops
0.022 - 0.028 for twin engine piston aircraft
0.020 - 0.030 for small single engine aircraft, retractable gear
0.025 - 0.040 for small single engine aircraft, fixed gear
0.06 for agricultural aircraft without spray system
0.070 - 0.080 for agricultural aircraft with spray system


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.