How is the zero-lift drag coefficient calculated?
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.