The first requirement is enough free space as to not cause interference or obstruction to your antenna. As much distance as possible in all directions, ideally many wavelengths. I used a field because I grew up on a farm, but you could use a public park, an empty beach, or common land.
The second requirement is for some means of measuring RF field strength. There are specialist instruments to do this, but for cheapness and practicality in this case I used an RTL SDR, one of those USB digital TV sticks. I plugged it into my Android tablet, ran the SDRTouch app, turned off the automatic gain control, and turned the gain down to about 10% of its range. My receive antenna was the nasty little 15cm wire antenna that comes with the SDR, the only time I've ever used it in action.
The third requirement is a transmitter. Any transmitter for the frequency of your antenna will allow you to take measurements, however for this practical test range you will need it to be capable of micropower output. I used a Raspberry Pi with my RF breakout board and an attenuator network. I calculated that my 47R-470R-47R Pi network resulted in an output around 0.03 mW, or 30μW. This resulted in a detectable RF field that was entirely within the boundaries of my range, in other words the transmitted signal was undetectable 100m from the antenna. For the purposes of legality I used a low-pass filter and a modified version of the freq_pi signal generator that inserted my callsign in CW into a continuous tone once every few minutes.
So, given my three prerequisites, I set to work. I set up my 2m HB9CV antenna in the middle of the field, chose an unoccupied frequency - a part of the repeater input segment not used in my part of the world - and fired up the Pi.
The detection setup was a clipboard with a piece of paper, and the tablet and receive antenna secured with rubber bands. I walked away from the antenna at each point of the compass, noting down the received signal strength at each metre interval.
My resulting figures could then be put into a spreadsheet and rendered as a radius plot to draw the radiation pattern for the antenna. And so I proved by measurement that an HB9CV is a directional antenna. Hardly unexpected, I'm sure you'll agree, but the real proof is that using a £20 single board computer and a £10 USB receiver it's possible to make real-world antenna performance measurements.