I'm sure which article you saw, but there is no rocket science to this. An
article by Ed Kolano that was in Sport Aviation in 2000 is available to EAA members on the EAA site.
First, you need good quality data. It helps to have an observer to record data, and watch for traffic, so you can concentrate on flying the aircraft accurately. Fly at a known weight, at a known CG. Plan to do several flights at the same weight and CG, so you can confirm that you have repeatable results. The results on any given day can be affected by rising or descending air due to the weather systems in the area. If you do testing on different days, the rate of climb you get will vary with OAT. But, if you are at the same weight and CG and altitude, you should get the same VX and VY if you plot the data from each flight individually (this assumes the OAT hasn't changed too much).
Choose a test altitude block that has smooth air and is clear of cloud. The accuracy of the testing will be increased as you increase the size of the altitude block - it would be good to have choose an altitude block that will take at least one minute to climb through. Do the climbs at 90 degrees to the expected wind direction at the test altitude. Do two climbs at each speed, with the second climb on a heading 180 different from the first one. This helps correct for small changes in wind as you climb.
Start the climb far enough below the lower end of the test altitude block, so that you are nicely stabilized at the test speed when you hit the bottom of the block. Start a stop watch when you hit the bottom of the altitude block, and record the time and altitude at several intervals as you climb. Record the time as you hit the top of the altitude block. Record the OAT at the bottom and top of the altitude block. Record fuel on board for each run. Record any notes on the quality of the test point.
After you land, for each run, plot altitude vs time. Draw a straight line through the points (choose the straight line that best fits the points), and measure the slope of the line to get the average rate of climb for that run. Average the rates of climb for the two runs at each speed speed. Plot the average rate of climb vs speed - speed on the horizontal axis, and rate of climb on the vertical axis. Draw a smoothed line through the data points. Expect that there will be a bit of noise in your data, so some points will not fall exactly on a smoothed line. If some points fall far from the line, review the notes for the two runs at that speed. Maybe there is a reason why the data at that speed is not like the others. VY is the speed at the top of the curve. Locate the place on the graph which represents zero speed and zero rate of climb, and draw a straight line from that point that just touches the plot of test data. The speed where this line touches the plot is VX.
There are ways you could further analyze the data to correct to standard weight and temperature, but that isn't really necessary if you just want to get VX and VY. Expect that both VX and VY will increase a bit as the weight increases.
There are ways to simplify the above test procedure. You could do only one run at each speed, but then the results will be affected by any changes in wind speed or direction as you climb. You could dispense with recording time and altitude at several intervals during each climb - just record the time for the whole altitude block. You could do forget about repeating the test on other days. Each simplification reduces the quality of the data, and the accuracy of the result. It is up to you do decide where the best balance lies between level of effort and accuracy of the result.
