Never ever have I seen a program so complicated to install... 

I purchased the program through itch.io (Tons of options... I just wanted to purchase the program. Why are there so many possibilities? I dont know this itch-thing and also not this tap-thing).

I finally managed to download it (was also not straightforward)

I installed it successfully

When I now start it, it says "Welcome to cider" and I can choose between "Sign in Cider Taproom" and then "Purchased through itch.io store". Then I click on "Authorize Cider". Then the Browser Shows "Welcome to the Taproom". The App itself says "Please continue in the browser window. Cider will automatically proceed once you've signed in."

Only it never does. It is stuck. There is a possibility to enter a tolken manually, but I don't know where to get this. I even checked cookies like I read in some other post, but I did not find the specified  cookie.

Finally I found the license key on tap-thingy-page and had the idea to enter it (I tried this several times, most of the times it showed 'undefinded' as a license key, but finally a license key was shown). It is absolutely straight forward to enter a 'License Key' to a field called 'Token'.  Please don't give one and the same thing the same name, it could confuse people.

I ask myself who designs such a process? Is this software developed just by Nerd developers without anyone who fulfills the role of a product owner, who has the user in mind? Or are there 5 product owners who overspecify everything? I just want to use the software. In todays world normally you press an install button and maybe you have to do one login. Here I have to use this itch.io and this taproom (I don't know what these two are and I dont want to learn just for using a software) and everything has to be linked together but it does not really work together.

I really recommend to radically clean up all of this.

The idea of a good apple music client sounds good though, especially if it works also on linux

I can concur, and also recommend a major cleanup and overhaul.

I have been using Cider for years now and have had to pay for this open source client twice as they continue to update their standards and distribution (part of this is Apple's fault for always changing their API, thus breaking the cider app everytime Apple makes a change). That being said, there is a lot left to be desired from a usability standpoint. I put up with a lot for a while during the beta, but it still feels "pre-alpha" levels of buggy at times, successful sign-in often requires multiple attempts (sign in via token doesn't work at all), and then, you need to restart the app in order to get the interface to properly load your library and *maybe* display your name. Also hovering over the side bar items affects the styling of other elements. A lot of questions, not a lot of answers.

Almost every time I've installed this app, be it on Linux or Windows, there is always some issue preventing sign-in or proper installation that has a "temporary fix" from the devs, posted via discord or the itch forums here... Until the next release breaks everything again, or they change their minds on the interface, CDN, or ecosystem AGAIN.

Yeah I agree with all of the above.  Absolute pain in the arse.  Make it much easier otherwise your going to continue to have issues with users trying to install.  Took 40 mins to install - should take 2 mins.  Pathetic really.  If you develop an app make it easy to install otherwise your wasting everyone's time and money.  

half of what you said is skill issues, but I do recognize that yeah the process is kind of a pain at the beginning. as a developer myself it was easy for me to download it as I had the usual developer intuition to find stuff, but I guess normal users would not be able to use it as straightforward as I did…