RGG FAQ Part 5 Section 3
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The usual convention is to label the Goban from left to right with letters from A to T (omitting 'I' to avoid confusion with '1') and from bottom to top (as seen by black) with numbers from 1 to 19.
In Japan, the coordinates are all numbers; arabic (1,2,3) along one axis, and Kanji along the other.
A move is then referred to by colour and position, e.g. Black E4.
When publishing moves (in e.g. a book or an article, or in a post to the newsgroup see also faq section 4.6) the most often used method is to represent (parts of) the Goban with numbers at the intersections.
In publication quality diagrams, black and white circles have move numbers inside them. Alternative moves or stones/moves discussed in the text are labelled with letters or symbols (triangles, etc.). Even publicationquality diagrams can get very crowded in a typical game (try finding move 131 in a diagram containing over 200 moves), so often they are broken up into multiple diagrams of 50 moves each, or fewer (the fewer moves per diagram, the easier the game is to read).
To record games by hand, there are preprinted sheets available with a 19x19 grid on them. As play goes on, you label each intersection with the move number. Some people use two pens with different colours (e.g. red and blue) for this, distinguishing black stones from white. Others put circles around the black moves, but not around the white moves, or similar. Notes such as "201 at 47" are made at the bottom for kos and other plays "under the stones" (playing on an intersection after the stone originally placed there is captured). This does become cumbersome after a while, though.
If you play on a computer, your program (player, or client) records the game for you. Games on the Go servers (see faq section 3.1.) are stored as SGF files; some programs use other formats as well (see faq section 6.2). Using a server's "automail" function, you can have all your games automatically emailed to you, for easy review with SGF viewer/editor software.
Programs which allow you to view, edit and comment these files exist for almost all operating systems. See faq section 6.1.