By measuring polarization of the received radio-frequency signals. The polarization is affected by magnetic fields ("Faraday rotation", see [0, 1]).

[0] https://en.wikipedia.org/wiki/Faraday_effect#In_the_interste...

[1] https://www.mpifr-bonn.mpg.de/research/fundamental/cosmag

> The image was made by combining data from multiple observations with the VLA's giant dish antennas arranged in different configurations to show both large structures and finer details within the galaxy. The naturally-emitted radio waves from the galaxy were analyzed to reveal the magnetic fields, including their directions.

In other words, this is a computer-generated image based on measured radio emissions and lots of modeling.

The papers linked in the article have a more detailed description of the methodology.