In Stone Age people wrote music in the caves or they will draw certain instruments on their walls, later these people they started to instead of drawing instruments they will draw different symbols, based on the music what they played at that time. Then first professional music schools will be open for special talents, not everyone can go in those schools. They learn their how to sing, play piano and different instruments, composition and how to write music as well.
Some famous composers will have their own transcribers, the composer will play musical piece and they will write music. Classical way of writing music took long time unless there were professional writers who they will write very fast, neat and beautiful. Today, thanks to technology and people who created computers and software, we can write music even we don't know anything about music, computer will do everything for us, we don’t need paper, pencil or music notebook, we don't need even music instrument at all to do that or to have any musical education.