My circuit and sketch can be found here.
http://justifiedandroid.co.uk/Dartuino
I pieced it together from a number of other sites such as this one.
http://www.martinpersson.org/wordpress/2010/08/electronic-darts-board-to-pc/
The dartboard face sits on top of two sheets separated by an insulating layer with holes under each segment. When a dart hits a segment the two sheets make contact completing the circuit. One sheet had 7 tracks, the other 10 creating a matrix (think grid with row/column) to map each segment to. For example single one could be 1/1, treble 20 could be 5/10, and bulls eye could be 7/8. Both single segments shared a cell so 70 is enough to cover the 62 possibilities.
It's basically this tutorial with a different multiplexer/demultiplexer.
http://playground.arduino.cc/learning/4051
The 4061 has more pins so I will be able to detect each segment (ie. 82 of them), and use the board's new game/bounce out buttons etc.
I thought the circuit would be the hard part, but the physical connection to the dartboard is proving more difficult. I've since ruined the acetate the dartboard's matrix circuit is printed on. I don't have any good ideas on how to replace it, or if I buy a new board or reliable way to connect my circuit to it.