Felix, piano technology is a much different world compared to playing and teaching the piano.
Many are surprised and find this hard to believe.
Piano tuning involves tempering or setting beat speeds between the various intervals. It is much too involved for me to write a treatise here. Bill Bremmer posts here in this forum. He has written some excellent articles and I am sure he will chime in and give you his web site. I do not recall and cannot find his site without interrupting this post. I suggest you read his articles to get an overview of what tuning entails. Though Bill's articles are very detailed, you can get an idea of what you are facing if you decide to learning tuning.
You asked about learning aural or purchasing a machine. You probably already know there has long been a fierce debate between aural tuners and tuners who use an ETD. My opinion, is aural tuning should be learned first. Most of the modern ETD's use the latest technology and are very very accurate. They can also be used to assist a new tuner to train his/her ear, but I (and many others) feel there is no substitute for a trained and experienced ear in conjunction with an ETD.
Repair is an essential part of tuning. I know people who "tune," but cannot repair and I would hesitate to call them a piano technician. Many are also limited in their ability to properly tune. Randy Potter has a correspondence course, I believe the web site is www.pianotuning.com
and is probably the best correspondence course available. Many here will probably elaborate upon my comments and furnish you with additional