You get a field strength the same way the pros do - from the antenna factors for your antenna and the cable loss. Look at a public FCC test report for an exposition of the method. DIY dipoles and even horns are not going to be very much different from ideal. Calibrated antennas are typically not more than a dB or two off ideal. Dipoles not even that unless they're broken. Horns and log-periodic antennas, enough that it can matter - but fine for hobbyist practice and even most pre-compliance work. I once discovered an RF engineer was using ideal gain numbers for a horn antenna instead of the calibration data for pre-compliance - it fortunately did not make a practical difference. The Roberts balun for measurement dipoles is standardized and I have instructions for building one around here somewhere. That is literally the reference for calibrating other antennas.
The primitive method for getting an antenna calibration is the three-antenna method. If you are particularly motivated, you can build three Roberts dipoles and check them. For a number of reasons, you might want to have three dipole kits anyway if you are doing a lot of these measurements.
"Tricky" in the sense that skiing is tricky. You will struggle learning from books and the internet. Starting from scratch with DIY equipment would be quite challenging. But it's all in standards and the open literature.