Designing step-up transformer
Although you could build your own high voltage transformer, the cost of the materials, will cost you more than buying/getting a scrap TV high voltage transformer.  In addition you save your time and effort.  

If you still want to build your own, you start with the output power.  Lets say you want 20KV at 0.01 amp,  p = 200W. Assume 80% efficiency, you then need 250W input.  your input current will be I = 250/300 = 0.8A, but for safety, you need 2A. The turns ratio is 67 (20k/300).
So, the input side should handle 300V @ 2A max. and the output should handle 20KV @ 20ma.
The rest of the calculations depend on the iron core that you get.  Be sure to get the spec sheet for the one you get.  Good Luck!