You need to complete the high level design of the game, decide how it will work.
Personally I think web games work best using a "tick-based" system which is similar to turn-based, but the players don't have individual turns, rather everything happens during a "tick" which affects all players.
You could run it from "cron", but if running every ten minutes, be VERY SURE that it has completed its previous run before starting the next one (consider using a file lock or other mutual exclusion mechanism to ensure it doesn't run multiple copies).
Your turn processor will probably take quite a while to run once you have a moderate number of players. You will want to ensure that the web interface is unavailable (or gives players a "please wait" message) while it's running.
There are a lot of fairness / cheating considerations to build in. In my opinion, players shouldn't have a significant advantage by continually hitting reload on some page - it will kill your server anyway if many do so.
You need to ensure that regardless of when during a tick (be it 10 minutes or 2 hours etc) a player hits the site, they have no advantage or disadvantage (other than having more time before the next tick to think about their game plan).
That way you give nobody any incentive to sit there hitting refresh waiting for the next tick.
Mark