I wrote a summary of the whole process on my website:

https://www.sionell.de/sioned/index.php/tips-und-tricks/72-griechische-yachtsteuer-t

German language only, sorry, but you might engage Google Translate...

There is also a comprehensive summary for members of the British Cruising Association in their member area with a lot of discussion about in the member forums.

@Rink:

You can pay either with a SEPA transfer from your bank account using the IBAN you find in the official FAQ or at one of the authorized collection agencies listed in that FAQ in cash. I would recommend an ELTA office as they seem to have the least problems.

As for non EU boats, as far as I know you have to pay through customs.