Well, to store the recurrence rule itself, you could use a cut down version of RFC 5545 (and I really suggest you cut it down heavily). Aside from anything else, that will make it easy to export into other applications should you wish to.
After you've made that decision, for the database side you need to work out whether you want to store each occurrence of the event, or just one record for the repeated event, expanding it as and when you need to. Obviously it's considerably easier to query the database when you've already got everything expanded - but it makes it trickier to maintain.
Unless you fancy writing some pretty complex SQL which may be hard to test (and you'll want a lot of unit tests for all kinds of corner cases) I would suggest that you make the database itself relatively "dumb" and write most of the business logic in a language like Java or C# - either of which may be embeddable within stored procedures depending on your database, of course.
Another thing you need to ask yourself is whether you need to cope with exceptions to events - one event in a series changing time/location etc.
I have some experience with calendaring (I've spent most of the last year working on the calendar bit of Google Sync via ActiveSync) and I should warn you that things get complicated really quickly. Anything you can deem "out of scope" is a blessing. In particular, do you need to work in multiple time zones?
Oh, and finally - be very, very careful when you're doing actual arithmetic with calendar operations. If you're going to use Java, please use Joda Time rather than the built-in Calendar
/Date
classes. They'll help you a lot.