The word 'azimuth' is kind of a giveaway that you're asking about a phono cartridge. :-)
I use the Wally Analog Shop to do this, and it is a great tool, but kinda pricey. Michael Fremer covers how to do this in the .PDF document that comes with his video, which I haven't seen. But in a nutshell...
You need a voltmeter and a test record with a band that plays a 1kHz tone into the Left channel and a band playing the tone into the Right channel. I use the Cardas Frequency Sweep test record - you can buy this wherever fine test records are sold.
Set the meter to low AC volts, 5V or less. Place the meter probes into your amp's left channel output terminals. Play the Left channel tone with the volume up enough to register around 2V. Get an average reading and write it down. Next, swap the probes to the amp's Right output terminals. Play the same Left channel tone and take an average reading and write it down - this is the 'bleedthrough' channel, the crosstalk.
Next, repeat the above procedure, but using the Right channel test tone.
You've got 4 readings in Volts. Convert the volts to decibels. The Wally tool includes a conversion chart to make this simple, or you can google for the formula. I believe the chart is available with the documentation that Wally has on his Web site. Look for Analog Shop and a .PDF file.
Once you've converted to dB, take the difference between the readings made with the Left channel test tone to give a number, then the difference for the Right channel test tone readings to give a number. Now you have two numbers. Adjust your cartridge's azimuth to get these two numbers within ... Here the relative difference depends on who you listen to, and how close you want your channel balance to be. I vaguely recall Fremer says within 10%. Wally says within 2-3dB is good, under 1.0dB is very good. I shoot for under 1.0dB because proper azimuth makes a big difference with my cartridge.
Basically you're aligning the stylus to maximize channel separation or minimize crosstalk. Keep an eye on the alignment of the stylus/cartridge. To get the proper numbers if it looks like the cartridge is really tilted, then something is wrong with the readings or the cartridge itself.
It also helps to equalize the output of your preamp before taking the crosstalk measurements. I probably shoulda written this first. You need a track with the 1kHz tone playing in *both* channels at the same time. (Cardas record has this.) Put the meter probes in the amp's left terminals, playing the 'both channels' track, and take a reading. Do the same for the right channel terminals. Then, adjust your preamp's balance control to get the same reading from both L and R amp terminals.
No doubt some golden-eared folks will come along and say you (they) can set azimuth by ear. Listen to a female vocalist who sings center stage. Adjust azimuth to get her mouth/voice as small/narrow as you can. Incorrect azimuth tends to splay sounds horizontally, making instruments and voices larger (spread wider) than they will be when azimuth is correct. This method can work too, though you need good sonic memory to make fine adjustments. I prefer the measured approach, if for no other reason that it is repeatable with accuracy.
The Wally Tool includes some low and high pass filters to smooth out the meter readings which tend to jump around as the needle traverses the groove.
Hope this makes sense. There are probably other methods, but this is the one I'm familiar with. Good Luck - proper azimuth can make a huge difference especially on more sensitive cartridges.
Tim