All the tango DJ’s I know have taught themselves the art. You can teach yourself, but DJing is a lot of work, and it takes a lot of study to become good at it, so don’t bother unless you seriously want to do it.
As I write this, on 3/14/20, most milongas have been cancelled, and most people are staying home. This is a perfect time to invest your time and energy into learning to DJ.
As preparation, I would recommend procuring a computer, software (I use iTunes) and tango music (I have 2879 songs; you can get by with 400 if they are the right ones; some DJ’s have many thousands). Organize the music by orchestras, and every other way that gives you fast and easy access. Make sure to record the tempo on every song, and the correct year of its original release. I use a software metronome, where you tap the space bar, get the tempo, and I refer to the Encyclopedia of Tango for dates and other details.
Collect background information on milonga programs. Analyze programs from other DJ’s, and try to figure out what they had in mind; compare with descriptions of how to build tandas, and how to construct milonga programs. Watch milongas, if possible, to see what songs are preferred in your area, and how effectively the DJ’s create a sense of Musicality and Connection with their music. In fact, teach yourself how to watch a couple dancing, and know whether they are connecting, or just practicing figures; figure out what is causing connection.
Learn about sound equipment, how to place speakers, how to overcome sound distortion and echo, and how to tweak the equalization for the best sound. Note the loudness of music at dances and other venues, with a Decibel app on your phone. Notice how well you can hear the beat of the music at various milongas, and how this affects your dance – especially your connection to your partner (I feel more freedom to improvise when I easily feel the music and don’t have to strain to detect the beat). Learn how to adjust your computer’s music player to equalize each song, and how to tweak volume, and how to add spacing. I recommend learning Goldwave sound editing software for editing music files.
When you are ready, offer to DJ at tango events. If you are in it to make money, you may have to wait a long time to find someone who will pay you when you have no track record. If you are in it to promote high quality music for tango, and money is not the issue, it may be easier to find a sponsor.