I worked on this a bit for the same reason (Sci Fi type book.) The system I came up with was 1 martian day = 1 sol (24.6 hours => we really luck out with this being so close.) 1 martian yr = 669.6 sols. I divided this up into 12 periods. 9 of them are 56 sols long (8x7), 2 are 55 sols long, and 1 is 55/56 sols long for the leap year that would occur 6 out of every 10 years.
As far as conversion, I don't think it would be done directly, except by computers. Every clock/wristwatch/etc. would need to display 2 different times, local time and 'Universal' time. On planets with a fairly earth-like period of rotation, like Mars, people would live and work on local time and use universal time when dealing with people from other planets. On a planet like Mercury with it's 88 day long 'days', everyone would probably just work off of universal time and local time would only be of interest for determining when you were on the sunny or dark side of the planet.