The subject of writing choreography almost seems to go against the art form. One would not necessarily think of writing anything down when it comes to dance. While there are no scripts, such as in theatre, a choreographed routine still needs structure and refinement. This starts in the mind of the choreographer and sometimes is put on paper before being worked out on the dance floor. "Written" choreography is more a mix of ideas, sketches and notes than it is a written document.
Picture visual images in your head of what the choreography should look like as you listen to a song or piece of music.
Name the steps of the dance movements so that you can write them down. Each movement should have its own name. These can be anything you want to call them.
Sketch visual interpretations of the dance movements next to the names you have given them. The sketches can be in any style as long as you understand them.
Mark moments in the song, or music, where you want certain dance moves to occur. Depending on the type of music you are writing to, there will be different ways of marking the movements in the piece. Classical, jazz and pop music all have different structures. Modern dance often isn't even performed to music, or is accompanied by spoken word. In this case the sketches of the dance movements alone would be arranged on paper. This is in accordance with the fact that "written" choreography is a mix of sketches and ideas.
Build sequences on paper that correspond to your vision of the choreography. The movements may be wildly divergent, or narrative in nature, depending on the music. Write down the names of the moves, or sketch the image of the dance moves next to your markings for the song movements. In the case of "writing" choreography to a non-musical piece, or minimalist piece such as spoken word, the document would look more like a shorthand drawing. Imagine it being arranged like a storyboard of dance movements.
Many choreographers do not formally write down their choreography. If so it is usually in a "working" form and not for presentation. Some modern dance choreographers study shorthand techniques that assign specific symbols to different parts of the body. This allows them to create choreography and share it with others who understand the same shorthand.